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1answer
82 views

A sphere, a simple object?

In this video, the woman says that a sphere is a pretty simple object. What intrigues me is the use of a sphere for such a calculation. First of all, the sphere wouldn't be perfect as a perfect sphere ...
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0answers
128 views

Approximations in simple pendulum

In the approximation $$-(g/ \ell) \sin \theta \approx -(g/ \ell) \theta $$ we make an error $R$ which is $O(\theta ^3)$. If i did well my calculations it is estimated by $$R\leq|(g / ...
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2answers
414 views

FWHM in resonance amplitude square derivation

Consider a linear harmonic oscillator subject to a periodic force: $$ \ddot x + 2 \beta \dot x + \omega _0 ^2x = f_0\cos \omega t$$ The solution tends to: $$A \cos (\omega t - \delta)$$ where: ...
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0answers
166 views

2D quantum well energy spectrum (analytical vs numerical)

I am trying to understand the energy spectrum difference between the analytical and the approximated solution for a quantum well. The particle is inside a box with domain $\Omega=(0,0)$X$(1,1)$. For ...
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3answers
1k views

Franck Condon Principle and Born Oppenheimer approximation

My question here is purely fundamental. I am confused with the concept in Franck Condon (FC) principle and Born Oppenheimer (BO) approximation. The FC principle is in accordance with the BO ...
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0answers
113 views

Measurement in Quantum mechanics

I have got a quantum conservative system whose Hamiltonian is $H$. I consider an selfandjoint operator $O$ whose eigenvalues and eigenvectors are: $$O|\psi _{n}\rangle = \lambda _{n}|\psi ...
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2answers
208 views

Computing microstate probabilities based on Boltzmann distribution for chemical systems - Is it rigorous?

One approach to predicting the folded structure of a polymer (DNA, RNA, protein) is to compute the probability that any particular part of the polymer $x_i$ is "paired" with another part of the ...
4
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2answers
400 views

WKB method of approximation

Would it be legitimate to use the WKB approximation for a particle in a spherically symmetric Gaussian potential? $$V(r)~=~V_0(1-e^{-r^2/a^2}).$$ I'm not sure when to use which approximation ...
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1answer
198 views

Hawking Radiation from the WKB Approximation

Reading this paper which is itself an exposition of Parikh and Wilczek's paper, I get to a point where I fail to be able to follow the calculation. Now this is undoubtably because my calculational ...
3
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4answers
170 views

Particles scattering on fluids: breakdown of the effective continuum description

When does the macroscopic continuum description of a medium like a fluid break down? Say I'm interested in a scattering process of some particles with momentum $p$ and energy $E$ off a fluid of ...
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4answers
1k views

Are Newton's three laws of motion correct?

New technology brings new ideas with these new ideas we have to look at the old ones. Where else is a better place to start then Newton's three laws of motion! With our common age of technology do we ...
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8answers
949 views

Why do physicists believe that particles are pointlike?

String theory gives physicists reason to believe that particles are 1-dimensional strings because the theory has a purpose - unifying gravity with the gauge theories. So why is it that it's popular ...
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1answer
171 views

Reference for understanding characteristic length and time scales in a system (in particular electronic transport)

I am working on the transport properties of two dimensional electron gas in semiconductor heterostructures and am interested in the characteristic length and time scales of the system like elastic ...
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3answers
334 views

Can a wavefunction be solved to any arbitrary precision, given enough computer time?

I learned that the wavefunction for the hydrogen atom can be solved analytically (we did the derivation in class), but that for more complicated atoms it is "impossible" to solve and that only ...
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1answer
515 views

Definition of elementary particle [duplicate]

Possible Duplicate: Why are atoms particles? According to wikipedia an elementary particle or fundamental particle is a particle not known to have substructure. Moreover, I've learned ...
2
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1answer
179 views

Zero entropy change

If you put a object in contact with a heat reservoir that is infinitesimally higher in temperature than the object and allow equilibrium to be reached the entropy change is zero right?
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3answers
164 views

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
211 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
117 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 ...
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1answer
118 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 ...
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0answers
161 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 ...
2
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1answer
357 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 ...
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3answers
238 views

Slow thermal equilibrium

I have a question which is inspired by considering the light field coming off an incandescent lightbulb. As a blackbody radiation field, the light is in thermal equilibrium at temperature $T$, which ...
1
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1answer
76 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 ...
2
votes
1answer
243 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
259 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 ...
3
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2answers
644 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 ...
5
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1answer
298 views

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 ...
3
votes
1answer
141 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 ...
3
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1answer
695 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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2answers
5k 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
141 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
277 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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5answers
3k 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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3answers
677 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 ...