Are Eigenkets with Eigenvalues Periodic for a Hamiltonian System?

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Homework Help Overview

The discussion revolves around the properties of eigenkets and eigenvalues in the context of a Hamiltonian system, specifically questioning whether the expectation values of observables will exhibit periodic behavior based on the given eigenvalues.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between the eigenvalues and the periodicity of expectation values, questioning the implications of rationality in the ratios of the eigenvalues.

Discussion Status

Some participants have provided insights regarding the conditions for periodicity, while others have raised clarifying questions about the meaning of relative rationality in this context. There is an ongoing exploration of the implications of the eigenvalues presented.

Contextual Notes

Participants are discussing the nature of the eigenvalues, specifically noting that two of them are irrational, which may affect the periodicity of the system's observables.

greisen
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Hey,

A Hamiltonian has 3 eigenkets with three eigenvalues 1, sqrt(2) and sqrt(3) - will the expectation values of observables in general be period functions of time for this system?

I don't know how to procede?

Thnaks in advance
 
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To be periodic the three frequencies must be relatively rational.
 
sqrt(2) is not a rational number neither is sqrt(3). So when you say relative rational what do you mean?

Thanks in advance
 
That their ratio is a rational number.
 
So I thought - so with the eigenvalues posted they will not be periodic!

Thanks for the replies
 

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