Probability of a wave function

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Discussion Overview

The discussion centers on the calculation of the probability of finding an electron in the ground state of a hydrogen atom, given its wave function in the context of quantum mechanics. The scope includes theoretical aspects of quantum mechanics and the mathematical formalism involved in wave functions and probability calculations.

Discussion Character

  • Technical explanation, Conceptual clarification

Main Points Raised

  • One participant asks how to find the probability of an electron in the ground state of hydrogen given its wave function.
  • Another participant suggests finding the projection of the given wave function onto the ground state wave function of hydrogen.
  • A third participant reiterates the projection method and expresses confusion about the reasoning behind this approach.
  • A later reply introduces the concept of wave functions as vectors in Hilbert space and states that the probability for one state to be in another is given by the formula ||^2.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the reasoning behind the projection method, as one participant expresses confusion about it.

Contextual Notes

The discussion does not clarify the assumptions underlying the projection method or the specific definitions of the wave functions involved.

soul
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Hi everyone,

Assume that we have an electron in the Coulomb field of a proton, whose wave function is specified. How can I find the probability of finding this electron in the ground state of the hydrogen atom?

Thank you.
 
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find the projection of that given wave function with the wave function of ground state for hydrogen.
 
malawi_glenn said:
find the projection of that given wave function with the wave function of ground state for hydrogen.

Why do we do that? I couldn't understand the reason.
 
It is the formalism of quantum mechanics?

Think of vectors in the plane, wavefuctions are vectors in Hilbert space.

The probability for state |a> to be in state |b> is given by: |<a|b>|^2
 

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