# Questions tagged [born-oppenheimer-approximation]

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### What are some of the practical system to which sudden approximation can be applied?

I've been trying to find the practical applications of sudden approximation but on one side, adiabatic approximation has a lot of practical applications but sudden approximation seems not to have any ...
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### Difference between Fixed Nuclei approximation, Born-Oppenheimer approximation, adiabatic nuclei approximation

I was reading some papers and depending on the author some would use the terms Fixed Nuclei approximation, Born Oppenheimer approximation, adiabatic nuclei approximation almost interchangeably whilst ...
1answer
43 views

### Correct indices on coupling matrix elements

Lets say i have an initial state $|i\rangle$ and a final state $|f\rangle$. A transition from $|i\rangle \rightarrow |f\rangle$ is coupled by an operator $\hat O$. Is the relevant coupling matrix ...
0answers
32 views

### Can the sign of non-relativistic potentials be determined from QFT amplitudes?

In many QFT books and courses people use a non-relativistic approximation to extract potentials from QFT. They do so by comparing the scattering in QFT with the scattering in Quantum Mechanics, in the ...
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### Why non-adiabatic matrix is an antisymmetric matrix?

In deriving coupling term beyond Born-Oppenheimer approximation, there is a term non-adiabatic coupling term written as: $$\tau_{ij} = \langle\zeta_i| \nabla\zeta_j\rangle$$ where $\zeta$ here is ...
1answer
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### About Born-Oppenheimer approximation

I was just going through random lecture notes on Born-Oppenheimer approximation where I came across the following statement: We first invoke the Born-Oppenheimer approximation by recognizing that, ...
2answers
215 views

### What is a nuclear wave packet?

What is the definition of a nuclear wave packet ? I often see the term used but i don't know how it is defined. It seems to be connected to the Born-Oppenheimer approximation. Is it defined there and ...
1answer
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1answer
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### Born-Oppenheimer Approximation equivalent to Tensor-product ?

If you have a wave function $\Psi$ of a system consisting of an electron and the vibrational modes of the crystal, THEN we represent the wavefunction $\Psi%$ to be in the Hilbert Space formed by the ...
1answer
358 views

### The Born-Oppenheimer approximation and muonic molecules

Does the Born-Oppenheimer approximation fail for muonic molecules (i.e. molecules where one or more electrons are replaced with muons)?