False: The Time Independent Hamiltonian Operator "H

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Discussion Overview

The discussion revolves around the interpretation of the statement regarding the time-independent Hamiltonian operator 'H' and its action on an "allowed state" Psi, specifically whether "H Psi=E Psi" holds true. The scope includes conceptual clarification and technical reasoning related to quantum mechanics.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • One participant asserts that the statement is false but does not provide a clear explanation for this conclusion.
  • Another participant questions the definition of "allowed state," suggesting it refers to possible physical states, including superposition states.
  • A third participant clarifies that an "allowed state" is a normalized superposition of eigenstates of the Hamiltonian, indicating that a general state is not necessarily an eigenstate.
  • One participant proposes that the answer could be "sometimes true, sometimes false," depending on the specific meaning of "allowed" in relation to energy eigenstates.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the interpretation of "allowed state" or the truth of the original statement, indicating multiple competing views remain.

Contextual Notes

The discussion highlights potential ambiguities in the definition of "allowed state" and the conditions under which the Hamiltonian operator acts on states, which may depend on the context of energy eigenstates.

mani5200
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Here is one of my test question. I did it wrong.

Specify whether the following statement is true or false and explain why? "The time independent Hamiltonian operator 'H' acting on an allowed state Psi will give the same state back, i.e "H Psi=E Psi, where E is the energy of the given state."

The answer is false. I don't know why but its false.

Can anyone explain me this?

Thank you.
 
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What does allowed state mean? If it means one of the possible physical states of the system and therefore superposition states are "allowed" then the answer is obvious.
 
An "allowed state" means a "physical state", and that is in general any (normalized) superposition of eigenstates of the Hamiltonian. So, a general state is not necessarily an eigenstate of the Hamiltonian.
 
The answer should be "sometimes true, sometimes false" unless "allowed" means specifically that the state isn't an energy eigenstate.
 

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