# Questions tagged [born-oppenheimer-approximation]

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### Hilbert space of a diatomic molecule

In molecular quantum mechanics, it is very common to model a diatomic molecule as a two-level harmonic oscillator with vibrational levels lying within the electronic states: In most of the textbooks ...
1 vote
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### Expected value of Hamiltonian with operators in atomic units [closed]

Hello I am currently working on a problem sheet for university, and am confused on how to solve it correctly. We deal with a helium atom and are asked to express the Hamiltonian in atomic units. This ...
72 views

### What steps are exact in Born-Oppenheimer and adiabatic approximation?

I am reading about adiabatic and Born-Oppenheimer approximation and I can't understand what steps are exact and what steps are approximations. Both these approximations are based on the idea that as ...
1 vote
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### Mathematical justification of the Born-Huang expansion in the derivation of the Born-Oppenheimer Approximation

In the book K. Huang and M. Born, Dynamical Theory of Crystal Lattices (1954, Appendix VIII) and also in the Wikipedia article https://en.wikipedia.org/wiki/Born%E2%80%93Oppenheimer_approximation#...
119 views

Born-Oppenheimer approximation leads to this equation for the eigenfunctions and eigenvalues describing molecular vibrations: $$\left[-\frac{\hbar^2}{2\mu}\frac{1}{R^2}\frac{\partial}{\partial R}\left(... 1 vote 1 answer 69 views ### Does the Born-Oppenheimer (adiabatic) approximation Ansatz allow excitations? The way I understand the Born-Oppenheimer approximation is as follows: In the general solid Hamiltonian for N electrons at 3N coordinates r and M ions at 3M coordinates R,$$ H = T_e + T_I ... 28 views

### 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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### Problems with a derivation of the Born-Oppenheimer approximation

I am trying to follow the derivation of the Born-Oppenheimer approximation proposed on Wikipedia. I know this is not the sexiest source, but i thought it could give a nice first glimpse. But actually,...
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### Why do only lattice vibrations contribute to the specific heat?

I would like to justify, that I can write the free energy of a real material (many-body system) at ambient conditions as $$F(T) = E_0^{\text{e}} + F^\text{v}(T)$$ where $E_0^{\text{e}}$ is the ...
312 views

### Hamiltonian in denominator

The second-order Born approximation for the scattering amplitude is given by $$f^{(2)}(k_f, k_i) = -\frac{m}{2\pi\hbar^2} \left<k_f\left| V \frac{1}{E-H_0+i\eta}V \right|k_i\right>,$$ where ...
1 vote
362 views

### Born-Oppenheimer approximation, electronic/nuclear wavefunction and product form

As I understand it, the main (or at least an important) statement of the Born-Oppenheimer Approximation is that the electronic and nuclear motion are separated and that the total wavefunction $\Psi$ ...
900 views

### Mathematical statement of the Born-Oppenheimer approximation

I have been looking up a formal mathematical definition of the Born-Oppenheimer approximation. I have thus far come across two (my wording): Definition 1 The Born-Oppenheimer approximation is ...
128 views

### Resource for Born-Oppenheimer approximation

I'm studying molecular physics but I'm failing in finding a good book with an accurate description of the Born-Oppenheimer approximation. I've tried some resource on the Internet and the McQuarrie's ...
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### Why does electron respond almost instantaneously on nucleus' displacement due to the difference in mass of it and the nucleus?

In Born Oppenheimer Approximation, we take note of the great difference between the mass of the electrons and nuclei. But, I have not been able to understand this statement quoted from Molecular ...
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### Solving Schrödinger's Equation for the electronic energies of the Molecular Ion Hydrogen H2+ in the Elliptic coordinate system

Electronic Energies of Molecular Ion Hydrogen $H_2^{+}$ $r_1$ is the distance between the proton $1$ and the electron. $r_2$ is the distance between the proton $2$ and the electron. $R$ is the ...
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### Form Factor in Rutherford Scattering

My question relates to Rutherford Scattering of particles. When we calculate the "differential cross-section" expression for a nucleus with finite size, it is said that the expression is almost the ...