What is lowest energy?











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In many textbook i come up with the term of lowest energy. For example in atomic structures electrons are placed in orbitals in order the atom to have the lowest energy? but what is this energy? potential or kinetic or the sum of the two?






quantum-mechanics energy hilbert-space ground-state







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    The sum of the two, usually the eigenvalue of the Hamiltonian operator.
    – Lewis Miller
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up vote
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In many textbook i come up with the term of lowest energy. For example in atomic structures electrons are placed in orbitals in order the atom to have the lowest energy? but what is this energy? potential or kinetic or the sum of the two?






quantum-mechanics energy hilbert-space ground-state







share|cite|improve this question




















  • 3




    The sum of the two, usually the eigenvalue of the Hamiltonian operator.
    – Lewis Miller
    5 hours ago













up vote
1
down vote

favorite









up vote
1
down vote

favorite











In many textbook i come up with the term of lowest energy. For example in atomic structures electrons are placed in orbitals in order the atom to have the lowest energy? but what is this energy? potential or kinetic or the sum of the two?






quantum-mechanics energy hilbert-space ground-state







share|cite|improve this question















In many textbook i come up with the term of lowest energy. For example in atomic structures electrons are placed in orbitals in order the atom to have the lowest energy? but what is this energy? potential or kinetic or the sum of the two?






quantum-mechanics energy hilbert-space ground-state




quantum-mechanics energy hilbert-space ground-state






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edited 5 hours ago









Qmechanic♦

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asked 5 hours ago









ado sar

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  • 3




    The sum of the two, usually the eigenvalue of the Hamiltonian operator.
    – Lewis Miller
    5 hours ago














  • 3




    The sum of the two, usually the eigenvalue of the Hamiltonian operator.
    – Lewis Miller
    5 hours ago








3




3




The sum of the two, usually the eigenvalue of the Hamiltonian operator.
– Lewis Miller
5 hours ago




The sum of the two, usually the eigenvalue of the Hamiltonian operator.
– Lewis Miller
5 hours ago










3 Answers
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2
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The sum of the two.



An electronic state like an orbital is an exact or approximate solution of some time independent Schrödinger equation, i.e. an eigenstate of the hamiltonian made by a kinetic and a potential energy term. The corresponding eigenvalue is the expectation value of such hamiltonian, evaluated on the state described by the orbital.



The expectation value of the hamiltonian can always be written as the sum of the expectation value of kinetic and potential energy. The lowest energy, is the eigenvalue of the hamiltonian with the minimum value.






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    The lowest energy of a quantum system is the minimum eigenvalue of the Hamiltonian of the system. The Hamiltonian is the operator which corresponds to the total energy of the system, so it is the sum of the kinetic and potential energy. This is often also referred to as the ground state energy of the system.




    but what is this energy?




    Heuristically, the ground state energy is the energy which the system has simply by existing. Normally, this doesn't make any sense: If I just make the system do nothing, just sit there, then it would have zero energy. We wouldn't need the fancy name.



    But it turns out that this is impossible. We can never "pin down" a system and make it completely still, due to the famous Heisenberg uncertainty principle,
    $$Delta x Delta p geq hbar/2.$$
    The system must have some momentum, to satisfy the inequality. In turn, it will also have some energy. This is why we can never reach absolute zero! No matter how hard we try, there always remains the jiggling of the ground state.






    share|cite|improve this answer




























      up vote
      1
      down vote













      In QM the Schrödinger Equation gives you the solutions for the wavefunction of a particle with a given potential. Because the energy is quantized you usually find several possible values for the energy that are given by an integer number $ n $ called the Principal Quantum Number. The lowest value of $ E_n $, normally when $ n=0 $ or $ n=1 $, is the Groud-State. This means that the energy of the particle is the lowest and it is a combination of the potential energy and the kinetic energy.






      share|cite|improve this answer





















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        3 Answers
        3






        active

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        3 Answers
        3






        active

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        active

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        The sum of the two.



        An electronic state like an orbital is an exact or approximate solution of some time independent Schrödinger equation, i.e. an eigenstate of the hamiltonian made by a kinetic and a potential energy term. The corresponding eigenvalue is the expectation value of such hamiltonian, evaluated on the state described by the orbital.



        The expectation value of the hamiltonian can always be written as the sum of the expectation value of kinetic and potential energy. The lowest energy, is the eigenvalue of the hamiltonian with the minimum value.






        share|cite|improve this answer

























          up vote
          2
          down vote













          The sum of the two.



          An electronic state like an orbital is an exact or approximate solution of some time independent Schrödinger equation, i.e. an eigenstate of the hamiltonian made by a kinetic and a potential energy term. The corresponding eigenvalue is the expectation value of such hamiltonian, evaluated on the state described by the orbital.



          The expectation value of the hamiltonian can always be written as the sum of the expectation value of kinetic and potential energy. The lowest energy, is the eigenvalue of the hamiltonian with the minimum value.






          share|cite|improve this answer























            up vote
            2
            down vote










            up vote
            2
            down vote









            The sum of the two.



            An electronic state like an orbital is an exact or approximate solution of some time independent Schrödinger equation, i.e. an eigenstate of the hamiltonian made by a kinetic and a potential energy term. The corresponding eigenvalue is the expectation value of such hamiltonian, evaluated on the state described by the orbital.



            The expectation value of the hamiltonian can always be written as the sum of the expectation value of kinetic and potential energy. The lowest energy, is the eigenvalue of the hamiltonian with the minimum value.






            share|cite|improve this answer












            The sum of the two.



            An electronic state like an orbital is an exact or approximate solution of some time independent Schrödinger equation, i.e. an eigenstate of the hamiltonian made by a kinetic and a potential energy term. The corresponding eigenvalue is the expectation value of such hamiltonian, evaluated on the state described by the orbital.



            The expectation value of the hamiltonian can always be written as the sum of the expectation value of kinetic and potential energy. The lowest energy, is the eigenvalue of the hamiltonian with the minimum value.







            share|cite|improve this answer












            share|cite|improve this answer



            share|cite|improve this answer










            answered 5 hours ago









            GiorgioP

            1,199212




            1,199212






















                up vote
                2
                down vote













                The lowest energy of a quantum system is the minimum eigenvalue of the Hamiltonian of the system. The Hamiltonian is the operator which corresponds to the total energy of the system, so it is the sum of the kinetic and potential energy. This is often also referred to as the ground state energy of the system.




                but what is this energy?




                Heuristically, the ground state energy is the energy which the system has simply by existing. Normally, this doesn't make any sense: If I just make the system do nothing, just sit there, then it would have zero energy. We wouldn't need the fancy name.



                But it turns out that this is impossible. We can never "pin down" a system and make it completely still, due to the famous Heisenberg uncertainty principle,
                $$Delta x Delta p geq hbar/2.$$
                The system must have some momentum, to satisfy the inequality. In turn, it will also have some energy. This is why we can never reach absolute zero! No matter how hard we try, there always remains the jiggling of the ground state.






                share|cite|improve this answer

























                  up vote
                  2
                  down vote













                  The lowest energy of a quantum system is the minimum eigenvalue of the Hamiltonian of the system. The Hamiltonian is the operator which corresponds to the total energy of the system, so it is the sum of the kinetic and potential energy. This is often also referred to as the ground state energy of the system.




                  but what is this energy?




                  Heuristically, the ground state energy is the energy which the system has simply by existing. Normally, this doesn't make any sense: If I just make the system do nothing, just sit there, then it would have zero energy. We wouldn't need the fancy name.



                  But it turns out that this is impossible. We can never "pin down" a system and make it completely still, due to the famous Heisenberg uncertainty principle,
                  $$Delta x Delta p geq hbar/2.$$
                  The system must have some momentum, to satisfy the inequality. In turn, it will also have some energy. This is why we can never reach absolute zero! No matter how hard we try, there always remains the jiggling of the ground state.






                  share|cite|improve this answer























                    up vote
                    2
                    down vote










                    up vote
                    2
                    down vote









                    The lowest energy of a quantum system is the minimum eigenvalue of the Hamiltonian of the system. The Hamiltonian is the operator which corresponds to the total energy of the system, so it is the sum of the kinetic and potential energy. This is often also referred to as the ground state energy of the system.




                    but what is this energy?




                    Heuristically, the ground state energy is the energy which the system has simply by existing. Normally, this doesn't make any sense: If I just make the system do nothing, just sit there, then it would have zero energy. We wouldn't need the fancy name.



                    But it turns out that this is impossible. We can never "pin down" a system and make it completely still, due to the famous Heisenberg uncertainty principle,
                    $$Delta x Delta p geq hbar/2.$$
                    The system must have some momentum, to satisfy the inequality. In turn, it will also have some energy. This is why we can never reach absolute zero! No matter how hard we try, there always remains the jiggling of the ground state.






                    share|cite|improve this answer












                    The lowest energy of a quantum system is the minimum eigenvalue of the Hamiltonian of the system. The Hamiltonian is the operator which corresponds to the total energy of the system, so it is the sum of the kinetic and potential energy. This is often also referred to as the ground state energy of the system.




                    but what is this energy?




                    Heuristically, the ground state energy is the energy which the system has simply by existing. Normally, this doesn't make any sense: If I just make the system do nothing, just sit there, then it would have zero energy. We wouldn't need the fancy name.



                    But it turns out that this is impossible. We can never "pin down" a system and make it completely still, due to the famous Heisenberg uncertainty principle,
                    $$Delta x Delta p geq hbar/2.$$
                    The system must have some momentum, to satisfy the inequality. In turn, it will also have some energy. This is why we can never reach absolute zero! No matter how hard we try, there always remains the jiggling of the ground state.







                    share|cite|improve this answer












                    share|cite|improve this answer



                    share|cite|improve this answer










                    answered 4 hours ago









                    Hanting Zhang

                    37216




                    37216






















                        up vote
                        1
                        down vote













                        In QM the Schrödinger Equation gives you the solutions for the wavefunction of a particle with a given potential. Because the energy is quantized you usually find several possible values for the energy that are given by an integer number $ n $ called the Principal Quantum Number. The lowest value of $ E_n $, normally when $ n=0 $ or $ n=1 $, is the Groud-State. This means that the energy of the particle is the lowest and it is a combination of the potential energy and the kinetic energy.






                        share|cite|improve this answer

























                          up vote
                          1
                          down vote













                          In QM the Schrödinger Equation gives you the solutions for the wavefunction of a particle with a given potential. Because the energy is quantized you usually find several possible values for the energy that are given by an integer number $ n $ called the Principal Quantum Number. The lowest value of $ E_n $, normally when $ n=0 $ or $ n=1 $, is the Groud-State. This means that the energy of the particle is the lowest and it is a combination of the potential energy and the kinetic energy.






                          share|cite|improve this answer























                            up vote
                            1
                            down vote










                            up vote
                            1
                            down vote









                            In QM the Schrödinger Equation gives you the solutions for the wavefunction of a particle with a given potential. Because the energy is quantized you usually find several possible values for the energy that are given by an integer number $ n $ called the Principal Quantum Number. The lowest value of $ E_n $, normally when $ n=0 $ or $ n=1 $, is the Groud-State. This means that the energy of the particle is the lowest and it is a combination of the potential energy and the kinetic energy.






                            share|cite|improve this answer












                            In QM the Schrödinger Equation gives you the solutions for the wavefunction of a particle with a given potential. Because the energy is quantized you usually find several possible values for the energy that are given by an integer number $ n $ called the Principal Quantum Number. The lowest value of $ E_n $, normally when $ n=0 $ or $ n=1 $, is the Groud-State. This means that the energy of the particle is the lowest and it is a combination of the potential energy and the kinetic energy.







                            share|cite|improve this answer












                            share|cite|improve this answer



                            share|cite|improve this answer










                            answered 41 mins ago









                            Kirtpole

                            1358




                            1358






























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