Average Potential Energy of a hydrogen 1s electron

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Homework Help Overview

The problem involves calculating the average potential energy of a hydrogen 1s electron using the potential energy operator V=e²/4πε₀r. Participants are discussing the necessary components and concepts related to this calculation.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are examining the potential energy operator and discussing the need for a minus sign in the expression. Questions arise regarding the relevance of the commutator of the Hamiltonian and potential energy operators, as well as the necessity of the Hamiltonian's form for the problem. There is also mention of calculating the expectation value of an operator as a potential approach.

Discussion Status

The discussion is active, with participants providing hints and questioning the assumptions made in the problem setup. There is acknowledgment of the complexity of the suggested method involving the virial theorem, indicating a range of interpretations and approaches being explored.

Contextual Notes

Participants note that the worksheet does not mention the commutator, raising questions about its necessity for solving the problem. There is also uncertainty about the complexity of the methods suggested for calculating the average potential energy.

condiboy
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I can't find any reference to this in my notes.

The problem is to calculate the average potential energy of a hydrogen 1s electron. The operator is V=e2 /4piE0r
 
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you forgot a minus sign. Also, what's the commutator of H and V?
 
good call on the minus sign. There's no mention of the commutator on the worksheet, is that necessary to know before doing the problem? I thought that the Hamiltonian operator for a hydrogen atom was -Hbar^2/2u-e^2/r. I'm really confused
 
I'll give a hint: How do you calculate the expectation value of an operator? I suspect that's what they want you to do.
 
alxm is right. I wanted you to use a method called the virial theorem in QM, but it might be too complicated.
 

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