Electron wavefunction as an overlap of orbitals

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Discussion Overview

The discussion revolves around the concept of the electron wavefunction as a superposition of atomic orbitals, specifically in the context of single electron atoms or ions. Participants explore the implications of this superposition for calculating average energy and measurement probabilities, while also seeking resources for further study.

Discussion Character

  • Exploratory, Conceptual clarification, Homework-related

Main Points Raised

  • One participant presents a problem involving the wavefunction of an electron expressed as a superposition of orbitals and requests resources for understanding this concept.
  • Another participant interprets "overlap" as "superposition" and notes that the answer would depend on a specific value of the coefficient ##a##, suggesting that expectation values are discussed in the participant's textbook.
  • A third participant emphasizes that the orbitals in the superposition are orthogonal, indicating that they do not overlap in the traditional sense.
  • The original poster acknowledges a misunderstanding regarding the terminology used and expresses intent to review their textbooks for relevant information.

Areas of Agreement / Disagreement

Participants generally agree on the terminology distinction between "overlap" and "superposition," but there is no consensus on the specifics of the problem or the best resources for further study.

Contextual Notes

The discussion highlights potential confusion around terminology and the mathematical treatment of wavefunctions, particularly regarding orthogonality and superposition in quantum mechanics.

WrongMan
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so I am finishing up my studies of intro to quantum mechanics, and this is not in my book and looking at previous exams i have to know this for single electron atoms/ions.
one of the problems was somethin like
"the wave function of an electron is the overlap of the orbitals:
Ψ=aΨ1s+i/√3Ψ2p+¾Ψ3s
find avg energy. what is the probability of measuring it?"
i don't want help solving this, can you just point me to an website/book that covers this? thank you
 
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"Something like" or "exactly like"? If I'm understanding the question properly by reading "overlap" as "superposition", it only makes sense for one particular value of ##a##. And (again, if I'm understanding the question properly) the answer is going to be in your book - somewhere it will talk about expectation values of measurements.
 
WrongMan said:
so I am finishing up my studies of intro to quantum mechanics, and this is not in my book and looking at previous exams i have to know this for single electron atoms/ions.
one of the problems was somethin like
"the wave function of an electron is the overlap of the orbitals:
Ψ=aΨ1s+i/√3Ψ2p+¾Ψ3s
find avg energy. what is the probability of measuring it?"
i don't want help solving this, can you just point me to an website/book that covers this? thank you
I wouldn't call it the "overlapp" but a superposition. The orbitals making up the superposition are orthogonal, so technically, they have no overlapp.
 
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Likes   Reactions: dextercioby
thanks for yur answers sorry about the overlap thing it was a translation problem.
and the problem i presentd was in an actual exam but all of them always have a problem like that.
im going to take a carefull look at both books I've got
 

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