Electron wavefunction as an overlap of orbitals

In summary, the student is studying quantum mechanics and has come across a problem on an exam that involves finding the average energy and probability of measuring a wave function for a single electron atom or ion. They are requesting a resource to help them understand this concept further.
  • #1
WrongMan
149
15
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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  • #2
"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.
 
  • #3
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.
 
  • Like
Likes dextercioby
  • #4
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
 

1. What is an electron wavefunction?

An electron wavefunction is a mathematical description of the probability of finding an electron in a particular location around an atom.

2. How is the electron wavefunction related to orbitals?

The electron wavefunction is related to orbitals because it is a mathematical representation of the electron's behavior in an orbital. It describes the probability of finding the electron in a specific orbital.

3. What is the significance of the electron wavefunction as an overlap of orbitals?

The electron wavefunction as an overlap of orbitals allows us to understand the behavior of electrons in molecules. It shows how electrons from different atoms can interact and form chemical bonds.

4. How do we determine the electron wavefunction of an atom?

The electron wavefunction of an atom can be determined using mathematical equations and quantum mechanics principles. It is a complex process that involves solving the Schrödinger equation for the specific atom.

5. Can the electron wavefunction change?

Yes, the electron wavefunction can change depending on the environment and interactions with other atoms. It is a dynamic property that describes the behavior of electrons in a given system.

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