Questions tagged [approximations]

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Why is current not 0 in a regular resistor - battery circuit immediately after you closed a circuit?

In regular open circuits with either a capacitor or inductor element, (when capacitor is uncharged) with a battery, when a switch is closed to complete the circuit the current is said to be 0 because ...
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3answers
266 views

In solving the hydrogen atom, how to see intuitively in advance that the spin effects to the energy spectrum can be ignored?

When the hydrogen atom is solved in QM books spin is usually ignored because its effect is to add tiny piece to the energy. My question is, is there a way to see this in advance, to see that if we ...
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2answers
152 views

A problem of approximation [duplicate]

Possible Duplicate: Why are continuum fluid mechanics accurate when constituents are discrete objects of finite size? When we apply differentiation on charge being conducted with respect to time,...
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1answer
146 views

Are Quantum Physics and statistical theory always the same as semiclassical approximations?

Quantum Mechanics and Statistical physics is a bit hard , could we then study only the WKB approximation ? In the form: replace $ \sum_{n=0}^{\infty}exp(- \beta E_{n})=Z(\beta)\sim\iint dxdpexp(-p^{...
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0answers
187 views

Hooke's Law and the shape of coils

I've learned in school that the force in a coil is $F=kx$, linear on how much the coil is stretched. Two questions: Is it always linear for every shape of a coil? Does it remain linear if we increase ...
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1answer
784 views

Proof of adiabatic theorem on Wikipedia

I'm having trouble following the proof of the adiabatic theorem (apparently due to Messiah) on Wikipedia. At one stage we have: $U(t_1,t_0)=1+{1\over i}\int_{t_0}^{t_1}H(t)dt+{1\over i^2}\int_{t_0}^{...
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1answer
93 views

semiclassical exact expression (in one dimension only)

let be $ N(x)= \sum_{n} H(x-E_{n}) $ the eingenvalue 'staircase' function and let be a system so $ V(x)=V(-x)$ and $ V^{-1}(x)=\sqrt \pi \frac{d^{1/2}}{dx^{1/2}} N(x) $ then would it be true that ...
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1answer
600 views

A missing factor of 2 in the standard Hartree-Fock mean field?

Let's start from a very simple argument: If $A$ and $B$ are some operators, then I can write their product as $$AB = (A-\langle A\rangle)(B - \langle B \rangle) + \langle A \rangle B + A \langle B \...
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3answers
416 views

Light Rays that are Perfectly Parallel

I just heard this simple reasoning in a documentary film: Light rays from distant stars are perfectly parallel. This is pretty interesting thought. In nature, it is hard to find something really ...
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2answers
2k views

Why are continuum fluid mechanics accurate when constituents are discrete objects of finite size?

Suppose we view fluids classically, i.e., as a collection of molecules (with some finite size) interacting via e&m and gravitational forces. Presumably we model fluids as continuous objects that ...
4
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1answer
190 views

Are energies non-transferable in the Born-Oppenheimer approximation, and when does it apply?

Adiabatic approximation or the Born-Oppenheimer approximation is used whenever the electronic motion is too fast that the electrons effectively see static nuclei and the nuclei, in turn, see an ...
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1answer
3k views

Time-Dependent Potentials in Quantum Mechanics

A potential that depends on time is usually solved using the time dependent perturbation theory in standard undergraduate textbooks in quantum mechanics. The reason usually mentioned is that time ...
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3answers
20k views

How is the Saddle point approximation used in physics?

I am trying to understand the saddle point approximation and apply it to a problem I have but the treatments I have seen online are all very mathematical and are not giving me a good qualitative ...
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0answers
175 views

Question on energies obtained via WKB approximation

Suppose we are given an ODE problem $$ y''(x)+V(x)f(x)=E_{n} y(x) $$ with boundary conditions $ y(0)=y(\infty)=0$. Here $V(x)$ is a potential function. Then is it always true that (for $n \...
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1answer
328 views

Using the Scalar Electrostatic Potential to Calculate Transition Probabilities

transition probabilites of atomic systems prone to some time-varying electromagnetic field are very often calculated using perturbation theory leading to expressions including the vector potential $\...
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7answers
32k views

Do we take gravity = 9.8 m/s² for all heights when solving problems? Why or why not?

Do we take gravity = 9.8 m/s² for all heights when solving problems?
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4answers
956 views

Special Relativistic approximation to GR

Some time ago I was talking to a professor in college about some of the fundamental aspects and origin of General Relativity. I was surprised to learn, in fact, that a pretty good approximation to GR ...
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1answer
1k views

What is the range of validity of Fermi's Golden Rule?

It is well known that to calculate the probability of transition in the scattering processes, as a first approximation, we use the Fermi golden rule. This rule is obtained considering the initial ...