Electron wavefunction as an overlap of orbitals

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SUMMARY

The discussion centers on the concept of electron wavefunctions as a superposition of orbitals in quantum mechanics, specifically for single electron atoms and ions. The wavefunction is expressed as Ψ=aΨ1s+i/√3Ψ2p+¾Ψ3s, where the user seeks resources to understand how to calculate average energy and measurement probabilities. Participants clarify that the term "overlap" should be replaced with "superposition," emphasizing that the orbitals involved are orthogonal and thus do not overlap. The conversation highlights the importance of expectation values in quantum mechanics for solving such problems.

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  • Understanding of quantum mechanics fundamentals
  • Familiarity with wavefunctions and superposition principles
  • Knowledge of orthogonal functions in quantum systems
  • Basic concepts of expectation values in quantum measurements
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  • Study the concept of superposition in quantum mechanics
  • Explore resources on calculating expectation values in quantum systems
  • Review the properties of orthogonal orbitals in quantum chemistry
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Students of quantum mechanics, particularly those studying single electron systems, educators teaching quantum principles, and researchers looking to solidify their understanding of wavefunctions and measurement probabilities.

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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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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