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1answer
575 views

Field from non-conducting plate?

For a non-conducting sheet, the electric field is given by: $$E = \frac{\sigma}{2\epsilon_0}$$ where $\sigma$ is the surface charge density. This equation holds well for a finite ...
3
votes
0answers
315 views

Born approximation to Lippmann-Schwinger integral equation

I am having the following problem understanding the Born approximation in the case of the Lippmann-Schwinger equation. This exercise is for something which is entitled "computational physics lab ...
1
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1answer
686 views

The Holstein-Primakoff Representation (approximation)

I have a question regarding the Holstein-Primakoff representation. In the HP-representation we define the spin operators in terms of bosonic creation and annihilation operators. $$ S_j^+ = \sqrt{2S ...
2
votes
1answer
412 views

Index of Refraction in Metal: Approximating Complex Perturbation

If you consider waves in a metal, you can write the index of refraction for the metal as, $$ n^2 = 1 - \frac{\omega_p^2}{\omega^2} $$ I am interested in what will happen if the index is perturbed by ...
6
votes
1answer
372 views

Adiabatic approximation

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 ...
7
votes
3answers
892 views

Finding the energy eigenvalues of Hydrogen using WKB approach

I need help to find the energy eigen values of Hydrogen atom using WKB approach. So far I know, the radial equation is given by $$\frac{1}{r^2} \frac{\partial }{\partial r} \left( r^2 \frac{\partial ...
3
votes
1answer
276 views

Can a very small portion of an ellipse be a parabola?

We consider that when a body is projected from any height from the earth surface with a speed lesser than the orbital speed ( tangentially to the earth surface at that point.) it follows an elliptical ...
3
votes
2answers
93 views

Can I alternate between notes really fast and have it sound like a chord?

The question basically amounts to whether I can construct the illusion of superposition with adjacent sine waves of varying frequency. Context I'm trying to play music on a Tesla Coil (like OneTesla ...
0
votes
1answer
485 views

When to use ideal gas law in fluid mechanics?

The ideal gas law (aka the equation of state) is given by $$ p/\rho_N = k_BT, $$ where $\rho_N$ is number density. When am I allowed to use this to describe a fluid?
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1answer
741 views

How to use the WKB approximation to find wave functions?

I'm trying to learn how to apply WKB. I asked a similar question already, but that question was related to finding the energies. Here, I would like to understand how to find the wave functions using ...
1
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1answer
1k views

How to apply the WKB approximation in this case?

I'm trying to learn how to apply the WKB approximation. Given the following problem: An electron, say, in the nuclear potential $$U(r)=\begin{cases} & -U_{0} \;\;\;\;\;\;\text{ if } r < ...
1
vote
1answer
98 views

Why does a difference in approach to projectile motion yields different results?

A body is projected vertically upwards from the surface of the earth with a velocity equal to half the escape velocity. If $R$ is the radius of the earth, then find the maximum height attained by the ...
2
votes
1answer
303 views

Finding the approximate solution for Schrodinger equation by using variational method [closed]

I need to find the approximate solution of nonlinear Schrodinger equation $$ i\hbar \partial_{t} \Psi + \frac{\hbar^{2}}{2m}\Delta \Psi - g |\Psi|^{2}\Psi - \frac{m\omega^2 (x^2 + y^2 + z^2)}{2}\Psi = ...
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votes
2answers
190 views

The nature of theoretical models

Mathematics is exact. It is a beautiful language that allows us to express quantities that aren't possible to be represented physically. We build theoretical models of physical systems that work out ...
1
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2answers
148 views

Discrete approximation of charge density

Given the electric potential $\Phi(r)$ and the Poisson's equation: $$ \nabla^2 \Phi(r) = - 4\pi \rho(r)$$ Consider the 2-dimensional case and let's say that I want to discretize this using a square ...
4
votes
1answer
711 views

Problem in Youngs double slit experiment

This is from Young Double slit experiment. But How to prove the the two $\theta$ are equal, I meant, how $\angle EAD= \angle PEC$? I see from the both triangle have $90^0$ but what about others?
3
votes
1answer
285 views

Neglecting second order differentials

I am currently doing some Lorentz invariance exercises considering infinitesimal Lorentz transformations, and have been told to neglect second order differentials. It's not the first time I have come ...
1
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0answers
158 views

Good book on deriving approximate solutions from first principles? [closed]

I have always been excited by examples in which a few simple assumptions and first principles are used to characterize a system. For example, I did an exercise in which Crawford estimates a lake to ...
4
votes
1answer
158 views

Solution of QM tasks by using asymptotics

When we solve QM tasks by solving the Schrödinger equation, such as tasks about a particle in a Morse potential, a Poschl-Teller potential and many others, we usually find approximations (lets call ...
3
votes
2answers
107 views

Any quadrupole approximation? Any example?

In atomic and molecular physics we quite often encounter with electric dipole approximation. The dipole approximation we do when the wave-length of the type of electromagnetic radiation which induces, ...
-1
votes
1answer
112 views

How can we depend on the mathematical axioms that break down at the nano-level? [duplicate]

Mathematics "makes sense" at our scope of view. For example, gravity seems to obey the fact that it accelerates at a rate of 9.8 meters a second^2. However, when an object drops, the force of gravity ...
5
votes
2answers
1k views

Small oscillations of the double pendulum

From the Lagrangian I've got the following equations of motion for the double pendulum in 2D. (The masses are different but the lengths of the two pendula are equal.) Let $m_2$ be the lowest-hanging ...
3
votes
1answer
307 views

Does effective theory have the same meaning in particle and condensed matter physics

I have a naive question about the meaning of effective theory in particle physics and condensed matter physics. In particle physics, from what I know, the effective theory comes from the Wilsonian ...
0
votes
2answers
73 views

Expand metric $g_{ij}$ about flat space

I expand metric $g_{ij}$ about flat space $\delta_{ij}$ $$g_{ij}=\delta_{ij}+h_{ij}$$ where $|h_{ij}|\ll 1$. I would like to find $R_{ij}$, to linear order, in terms of $h_{ij}$, but I dont know ...
0
votes
0answers
100 views

How to get general relativity from linear gravity theory?

I know someone had done this study. Namely the field approach to general relativity. We can easily get an linear gravity theory. But it will be very complicated when we consider the ...
4
votes
1answer
89 views

What kinds of contributions can be neglected in the leading logarithmic approximation?

I'm looking for some good explanation on leading logarithmic approximation (LLA) in QCD; in particular, what types of contributions can be neglected while assuming LLA?
3
votes
1answer
283 views

'Validity' of QED/QCD/Electroweak interaction

I am currently attending a course on Quantum Field Theory and I got into thinking how valid these theories are. As the theory attempts to describe reality only far above the Planck (length) scale, ...
1
vote
1answer
98 views

How can we consider charge to be continuous? [duplicate]

In electrostatics, we usually consider charge to be continuous on any body, to calculate the electric field of the body. For eg. I had proved the Shell Theorem taking an infinitesimal charge of $dq$ ...
1
vote
1answer
361 views

Schrödinger equation for many body systems

$$H_{tot}=\sum \dfrac{p_i^2}{2m}+\sum\dfrac{p_I^2}{2M_I}+\sum V_{nucl}(r_i)+\dfrac{1}{2}\sum_{i\ne j} \dfrac{e^2}{|r_i-r_j|}+\dfrac{1}{2}\sum_{I\ne J}\dfrac{z_Iz_Je^2}{|R_I-R_J|} $$ with: ...
3
votes
1answer
410 views

Self-consistent field approximation and uniform field approximation?

Can anyone give me explanation of self-consistent field approximation and uniform field approximation? I know self-consistent as when we write the Schrödinger equation as $$[ -\frac{\hbar^2}{2m} ...
1
vote
1answer
116 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 ...
5
votes
2answers
203 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 / ...
0
votes
2answers
806 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: ...
1
vote
0answers
305 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 ...
1
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0answers
126 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 ...
2
votes
2answers
269 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 ...
5
votes
2answers
539 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 ...
5
votes
1answer
285 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 ...
5
votes
4answers
204 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 ...
-1
votes
4answers
3k 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 ...
10
votes
7answers
2k 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 ...
1
vote
1answer
264 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 ...
3
votes
3answers
419 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 ...
1
vote
1answer
977 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
votes
1answer
314 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?
1
vote
3answers
221 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 ...
1
vote
3answers
241 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 ...
3
votes
2answers
131 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 ...
2
votes
1answer
128 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 ...
1
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0answers
174 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 ...