# Questions tagged [approximations]

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### When is the adiabatic approximation for solid state systems valid?

The adiabatic approximation for solid state systems is rather radical. I was wondering in which cases it breaks down. As it is based on the idea of the nuclii being much heavier than the electrons I ...
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### Phase-shifting of instantaneous eigenstates in the adiabatic approximation

In my book Quantum Mechanics by B.H. Bransden and C.J. Joachain, there is a chapter on the adiabatic approximation. Here, the authors assume that the time-dependent Hamiltonian $\hat{H}(t)$ changes ...
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### Planck's theory question

Could you please tell me why Planck's theory ceases to be valid when the sizes of the bodies and/or their separation distances are comparable to, or smaller than, the wavelength. My professor told me ...
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### Idealizations of an object as a point particle

Why is it that an object can be idealized as a point particle or 'particle like' to solve problems? What are the limits of such a tool?
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### Hyperfine structure in hydrogen

Consider the Dirac equation for bounded electron in hydrogen atom. I am trying to get a clear physical explanation for all mathematical terms that appear in the Hamiltonian and energy spectrum. ...
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Some context: I'm having a hard time deriving the results of the Hartree-Fock approximation. Let $H$ have the form $$H = \sum_{i=1}^{n}\left[\frac{p_{i}^{2}}{2 m}+U\left(\vec{r}_{i}\right)\right]+\... 0answers 61 views ### Does uncertainty principle truly represent the “lower bound” of the information we can obtained from a pair of noncommunicable operator? Background I: Suppose the commonly used non commuting operator \hat p and \hat x. The uncertainty principle told us that \sigma_p\sigma_x\geq \frac{\hbar}{2}. In standard quantum mechanic ... 0answers 91 views ### Perturbation to the flat space metric from the geodesic equation for non-relativistic case where$$v_i\ll c\frac{dx^i}{dt}\ll1,{\rm for }\ c =1\frac{dx^i}{d\tau}\ll\frac{dt}{d\tau}$$using this the geodesic equation for proper ... 0answers 50 views ### How do we understand the results of 1/N or \epsilon expansion beyond leading orders? When we do 1/N expansions in, say, 2+1D O(N) models and try to extract all kinds of critical exponents from it, we get the following results for the scaling dimensions of various operators up to ... 2answers 129 views ### Series expansion of N-particle potential energy I am trying to understand the so-called Taylor expansion (or series expansion) of potential energy of a system of N-particles. This expanded form is stated without derivation in some molecular ... 0answers 73 views ### Time-independent perturbation theory: why i'th order perturbations are orthogonal to base state? I have been learning about time independent perturbation theory (non-degenerate for the moment), and am not satisfied about a particular point: the justification for setting \langle n^i|n^0\rangle = ... 0answers 86 views ### Is there any approximation in which the double pendulum has an exact solution? We know that the double pendulum isn't an integrable system, since only energy is conserved versus two degrees of freedom. My question is, does a physical approximation exist, in which the total time ... 0answers 103 views ### Is there an easy way to understand why doubly excited helium does not exist? 1) A method for evaluating the energy of helium states To understand why doubly excited helium is not allowed in nature, we should show, to my eyes, that if we try to build this state we'll find a ... 0answers 46 views ### pNRQCD at high pT pNRQCD is an effective field theory for heavy Quarkonium, where the velocities are non-relativistic due to large mass. But is pQCD applicable when the Quarkonium is moving at high velocities? The ... 0answers 504 views ### What can be an example or a scenario where the continuum definition of fluid mechanics would not be valid? The continuum definition of fluid mechanics may not be valid if a system contains too few molecules cause properties such as density, concentration and velocity are not well defined at a mathematical "... 0answers 72 views ### How to show transfer integral is a real number? I want to know how to show transfer integral is a real number. I am learning tight binding approach. Now let's consider the two-dimensional system whose unit cell has two atoms (for example, ... 1answer 124 views ### Ohms law hold till what temp? Is the Ohm's law verified to hold true at all temperatures? If not, then till what temperature does the Ohm's law hold? I think it is valid only till 0 K and above. Am I right in my thinking? 0answers 77 views ### Validity of Ising model for mean field thoery The Heisenberg model for the Hamiltonian of a ferromagnet is given by:$$H=-\frac{J}{2} \sum \vec{S}_i\cdot \vec{S}_j+\mu_B B \sum_i S^z_i when performing mean field theory, to find $\chi$, we ...
I want to add friction forces to my computer game. I know there are tables for friction, however I don't think that encoding big table of coefficients (of size $n^2$) is a good idea. I thought, that ...