Does it matter which eigenvectors

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    Eigenvectors Matter
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Discussion Overview

The discussion revolves around the significance of eigenstates and eigenvalues in the context of the Schrödinger equation in quantum mechanics. Participants explore whether the choice of eigenstate matters or if only the eigenvalue is relevant, touching on concepts of normalization and physical measurability.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant notes that finding an eigenstate ψ implies that any scalar multiple c*ψ is also an eigenstate, questioning the importance of the choice of eigenstate versus the eigenvalue.
  • Another participant emphasizes the requirement for normalization of states, stating that the overall complex phase can be chosen freely since it is not physically measurable.
  • A participant asserts that the state contains all the information in quantum mechanics, while eigenvalues only provide probabilities, suggesting that the state is of primary importance.
  • Another reiterates the idea that eigenvalues are measurable quantities in experiments, implying a distinction between the significance of states and eigenvalues.
  • There is a claim that the eigenvalue of a particular eigenstate represents the probability of that state, though this is challenged by another participant who questions the interpretation of eigenvalues as probabilities.

Areas of Agreement / Disagreement

Participants express differing views on the importance of eigenstates versus eigenvalues, with some emphasizing the primacy of the state and others focusing on the measurability of eigenvalues. The discussion remains unresolved regarding the implications of these perspectives.

Contextual Notes

There are unresolved assumptions regarding the definitions of eigenstates and eigenvalues, as well as the interpretation of probabilities in quantum mechanics. The discussion also reflects varying interpretations of the physical significance of overall phase in quantum states.

aaaa202
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If you solve the Schrödinger equation time independent and find a number of stationary position states they are eigenstates. So say uou find the eigen state ψ then c*ψ is also an eigenstate, Does it matter which of these I pick as the eigenstate or is it only the eigenvalue that matters?
 
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We generally require our states to be normalized. This still let's you choose the overall complex phase of the state. You can take this phase to be anything you want, because the overall phase is not physical (i.e., not measurable).
 
By the First postulte of Quantum Mechanics, state is the most important thing, it contains all the information that can be known, eigen value will give you just the probability, state is what we really intend to look for!
 
sugeet said:
By the First postulte of Quantum Mechanics, state is the most important thing, it contains all the information that can be known, eigen value will give you just the probability, state is what we really intend to look for!
Eigenvalues are what one can measure in experiments.
 
eigen value of a particular eigen state, its the probability of the state!
 
sugeet said:
eigen value of a particular eigen state, its the probability of the state!
Are you thinking of expansion coefficients? The eigenvalues are not probabilities.
 

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