Evaluate the commutator P:, [P:, H]] , where pz is the z-component of the momentum operator and H = . +V(r) is the Hamiltonian of the system. Use this result to prove the following sum rule: (En – Em)|(n|p: |m)|² - Σ %3D 2 where n) and |m) are eigenvectors of H with eigenvalues En and Em; respectively.
Evaluate the commutator P:, [P:, H]] , where pz is the z-component of the momentum operator and H = . +V(r) is the Hamiltonian of the system. Use this result to prove the following sum rule: (En – Em)|(n|p: |m)|² - Σ %3D 2 where n) and |m) are eigenvectors of H with eigenvalues En and Em; respectively.
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![Evaluate the commutator
P:, [P:, H]],
_p²
where pz is the z-component of the momentum operator and H =
Hamiltonian of the system.
2m +V(r) is the
%3D
Use this result to prove the following sum rule:
Σ
E(En – Em)|(n|p:|m)|² = 5 (m
%3D
m
-
where |n) and |m) are eigenvectors of H with eigenvalues En and Em; respectively.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F75f6df43-99e5-49ed-a68c-ec07e10ce1e5%2Fa44b4ade-feb6-432a-b9aa-1be6657fa1e7%2Fc7f6s0t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Evaluate the commutator
P:, [P:, H]],
_p²
where pz is the z-component of the momentum operator and H =
Hamiltonian of the system.
2m +V(r) is the
%3D
Use this result to prove the following sum rule:
Σ
E(En – Em)|(n|p:|m)|² = 5 (m
%3D
m
-
where |n) and |m) are eigenvectors of H with eigenvalues En and Em; respectively.
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