Probability of a wave function

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To find the probability of an electron in the ground state of a hydrogen atom, one must project the given wave function onto the ground state wave function. This involves calculating the inner product of the two wave functions, represented as |<a|b>|^2. Understanding this projection is essential as it aligns with the formalism of quantum mechanics, where wave functions are treated as vectors in Hilbert space. The concept of probability in quantum mechanics is fundamentally tied to these projections. Thus, mastering this technique is crucial for analyzing quantum states effectively.
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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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