The approximations tag has no wiki summary.
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1answer
53 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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59 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 $$R\leq|(g / ...
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1answer
73 views
FWHM in resonance amplitude square derivation
Consider a linear harmonic oscillator subject to a periodic force:
$$ \ddot x + 2 \beta \dot x + \omega _0 ^2x = f_0\cos \omega t$$
The solution tends to:
$$A \cos (\omega t - \delta)$$
where:
...
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0answers
73 views
2D quantum well energy spectrum (analytical vs numerical)
I am trying to understand the energy spectrum difference between the analytical and the approximated solution for a quantum well.
The particle is inside a box with domain $\Omega=(0,0)$X$(1,1)$. For ...
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3answers
458 views
Franck Condon Principle and Born Oppenheimer approximation
My question here is purely fundamental. I am confused with the concept in Franck Condon (FC) principle and Born Oppenheimer (BO) approximation. The FC principle is in accordance with the BO ...
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33 views
Approximating a first order ODE when the Hessian is available [closed]
I'm attempting to numerically approximate a simple ODE, I'm using it to describe the motion of a gradient descent search, but it could easily have physical interpretation. In particular,
$$
x'(t) = ...
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47 views
What is the difference between Mean Field Theory and Effective Medium Theory?
I understand that Effective Medium Theory (EMT) is a kind of Mean Field Theory (MFT), but I am unclear about the distinction.
What are the defining characteristics of a Mean Field Theory?
What ...
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0answers
86 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: $$O|\psi _{n}\rangle = \lambda _{n}|\psi ...
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2answers
122 views
Computing microstate probabilities based on Boltzmann distribution for chemical systems - Is it rigorous?
One approach to predicting the folded structure of a polymer (DNA, RNA, protein) is to compute the probability that any particular part of the polymer $x_i$ is "paired" with another part of the ...
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2answers
244 views
WKB method of approximation
Would it be legitimate to use the WKB approximation for a particle in a spherically symmetric Gaussian potential?
$$V(r)~=~V_0(1-e^{-r^2/a^2}).$$
I'm not sure when to use which approximation ...
4
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1answer
130 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 ...
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3answers
383 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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594 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
76 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
223 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
251 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 ...
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1answer
83 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
105 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
139 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
91 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
97 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
94 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 ...
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1answer
201 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
172 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 ...
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1answer
68 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
136 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
161 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
300 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
265 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 ...
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1answer
114 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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2answers
2k 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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124 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
204 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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565 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 ...
