I Electron wavefunction as an overlap of orbitals

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
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. Towards the end of the first lecture for the Qiskit Global Summer School 2025, Foundations of Quantum Mechanics, Olivia Lanes (Global Lead, Content and Education IBM) stated... Source: https://www.physicsforums.com/insights/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect/ by @RUTA
If we release an electron around a positively charged sphere, the initial state of electron is a linear combination of Hydrogen-like states. According to quantum mechanics, evolution of time would not change this initial state because the potential is time independent. However, classically we expect the electron to collide with the sphere. So, it seems that the quantum and classics predict different behaviours!

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