The tag has no wiki summary.

learn more… | top users | synonyms

1
vote
0answers
33 views

WKB Quantization Condition - negative?

In deriving the quantization condition for a bound state in a potential with "no verticle walls" we start with the WKB connection formulas to find the wavefunction in the interior of the well ...
2
votes
0answers
53 views

WKB formula and Langer correction [duplicate]

The general WKB approximation formula states that $$ \int_a^b\sqrt{E_k-V(x)} = (k+1)\pi \text{ with } x \in [a,b] $$ for a regular Schrödinger equation (without the $\hbar$ and such). However, in the ...
2
votes
2answers
46 views

Temperature in statistical mechanics and differentiating entropy

In statistical mechanics, the entropy of an isolated system with energy $E$ (with fixed volume $V$ and chemical composition $N$) is defined as $S(E) = k \log \Omega$, where $\Omega$ is the number of ...
1
vote
1answer
52 views

Magnetization $\ M$ of a ferromagnet as a function of temperature $T$, nearby $T=0$

Using mean-field theory, the magnetization per spin, $M$, for a ferromagnet always obeys the equation: $M=\frac{g \mu_{\mathrm{B}}}{2}\mathrm{tanh} \left( \frac{2}{g \mu_{\mathrm{B}}} ...
1
vote
1answer
30 views

What do we get from the diagonalization of the $k\cdot p$ matrix?

In k.p theory, we expand the wave function around a known point ${\bf k}_0$ $$u_{\lambda}({\bf k})=\sum_{\nu} c_{\lambda,\nu}({\bf k})u_{\nu}({\bf k}_0).$$ If we now consider 8 bands (conduction, ...
1
vote
1answer
39 views

Post-Newtonian approximation for binary gravitating system

I have been studying gravitation waves radiated by a binary source. I have linearised Einstein's field equation and approximated the source to a Quadrupole moment to get the power radiated by the ...
11
votes
5answers
1k views

If the solar system is a non-inertial frame, why can Newton's Laws predict motion?

Since there is no object in the universe that doesn't move, and the solar system likely accelerates through space, how did Newton's Laws work so well? Didn't he assume that the sun is the ...
2
votes
0answers
20 views

How can the fictitious mass in the Car-Parrinello method reproduce the “real” dynamics?

In the Car-Parrinello method, to solve simultaneously the classical equations of motion for the atoms and the Kohn-Sham equations for the electrons, the following effective Lagrangian is used: $$ ...
7
votes
2answers
512 views

What will be the equation of motion of driven pendulum for amplitudes beyond the small angle approximation?

When finding the period of a pendulum beyond the small angle approximation, we have to use integration for small interval of $\theta$ and elliptical integration. I was trying to apply this situation ...
3
votes
3answers
407 views

What's the difference between “numerical methods” & “mathematical analysis” as said by Feynman in his lectures?

While reading his lectures, I came to these lines: On the basis of Newton's second law of motion,which gives the relation between the acceleration of any body & the force acting on it,any ...
0
votes
1answer
26 views

Time Dependent Perturbation Theory Probabilities

(This is taken from Griffiths Quantum Mechanics): So suppose I have two states $\psi_{a}$ and $\psi_{b}$, and the particle starts out in the state $\psi_{a}$: $$ c_{a}(0)=1\qquad c_{b}(0)=0. $$ To ...
1
vote
0answers
40 views

Applying Statistical Mechanics to Formulate Corrosion (Rusting)

I wanted to try and take my current knowledge of statistical mechanics (first quarter undergraduate course completed, beginning researcher in far from equilibrium statistical mechanics, basic ...
3
votes
3answers
602 views

Why do we use the Coulomb potential for the hydrogen atom?

When solving the Schrodinger equation for the hydrogen atom, the Coulomb potential $V = \frac{e^2}{4 \pi \epsilon_0 r}$ is used. The Coulomb potential comes from classical electrodynamics, so why ...
2
votes
0answers
63 views

Why does the time-independent perturbation theory become no longer useful when its order gets larger?

In Griffith's Introduction to Quantum Mechanics p. 256, after figuring out $$E_n^2=\sum_{m\neq n} \frac{|\langle\psi_m^0|H'|\psi_n^0\rangle|^2}{E_n^0-E_m^0}$$ he says We could go on to calculate ...
2
votes
2answers
82 views

Derivation of velocities in the Coriolis force

In Fitzpatrick's Newtonian Dynamics book on the Coriolis force, he states \begin{align} v_{x'}&\simeq V_0\cos\theta-2\Omega t V_0\sin\lambda~\sin\theta \tag{433}\\ ...
0
votes
0answers
26 views

Atmospheric refraction approximation

I am studying atmospheric refraction, reading ITU P.834 Effects of tropospheric refraction on radiowave propagation, and I have a question about an approximation. They say that refraction correction, ...
3
votes
1answer
370 views

WKB approximation for multiple turning points

I'm working on a numerical program which approximates the eigenvalues of a Schrödinger equation by making use of the WKB approximation formulas. For example, if the Schrödinger equation is $$ y''(x) = ...
1
vote
0answers
50 views

Does Planck's constant imply limits to computing *results*

... I don't mean quantum effects limiting hardware fabrication sizing. Such small scales have for some time exhibited issues. Rather, along the lines of imagining the smallest possible divisions of ...
3
votes
2answers
98 views

Mathematical approximation to physics

Why is it often said that any mathematical theory is just an approximate theory of the universe? Wouldn't there be accurate mathematical structures repressing the physical entities of the universe ...
1
vote
1answer
57 views

Electron electric field

As we know the fundamental unit of charge in our universe at the time of electrodynamics was an electron, and in any frame of reference, its radius is a finite number and assuming uniform charge ...
1
vote
1answer
101 views

How to reconcile these two approximations?

I'm working on what should be a simple problem (Taylor Classical Mechanics problem 6.23.), but I'm having a tough time reconciling the many ways it can be tackled. An aircraft whose speed is $v_0$ ...
3
votes
3answers
105 views

Solving differential equations without approximations?

In physics, many problems start with a mathematical relationship of the physical phenomenon at hand, and then, in many occasion, always only leave whatever in the first order to get a nice and ...
2
votes
1answer
79 views

Why do we consider the electric field of an infinite plane? [closed]

I never understood why one would calculate the electric field surrounding an infinite plane, if such thing does not exist. Is there physical motivation for using this model? Are the results applicable ...
2
votes
3answers
151 views

Singularity in Newton's gravitational law [duplicate]

If $r=0$ in the well know equation $F= G\dfrac{m_1\cdot m_2}{r^2}$, it will not follow that the force will be infinite? May someone please clarify it to me?
3
votes
0answers
146 views

What does it mean to expand a Hamiltonian using perturbation theory?

On UC Davis chemwiki website, the Hamiltonian for quadrupolar coupling in NMR is analyzed. (The details of this aren't important.) It is said in the analysis that: The expansion of the ...
2
votes
1answer
154 views

Proof of the conservation of the energy functional for the Gross-Pitaevskii equation?

From the Gross-Pitaevskii equation \begin{equation}i\hbar\frac{\partial\psi}{\partial t}=\left(-\frac{\hbar^2}{2m}\nabla^2+V+g|\psi|^2\right)\psi\end{equation} using the variational relation ...
3
votes
1answer
83 views

Evaluating low-temperature dependence of the BCS gap function

How does one go about evaluating the behavior of the BCS gap $ \Delta = \Delta(T) $ for $ T \to 0^+ $ under the weak coupling approximation $ \Delta/\hbar\omega_D \ll 1 $? In Fetter & Walecka, ...
2
votes
2answers
251 views

Is gravitational potential energy proportional or inversely proportional to distance?

We know that if an object has been lifted a distance $h$ from the ground then it has a potential energy change: $$\Delta U = mgh $$ so $h$ is proportional to $\Delta U$. However, we have also the ...
9
votes
3answers
381 views

What does Feynman mean when he says that $F=ma$ is not exact?

Chapter 12-2 in Feynman Lectures Vol. 1 states: In fact the law, $F=ma$ is not exactly true; if it were a definition we should have to say that it is always true; but it is not ... First, ...
0
votes
0answers
13 views

Modelling of nuclear motions (Classification) after invoking the BO approximation

I know that after invoking the Born-Oppenheimer approximation, the nuclei will move on the adiabatic potential provided by the electronic energy (also called potential energy surface (PES)). Such ...
1
vote
2answers
88 views

Taylor series: Epsilon not differentiated? [closed]

Why isn't epsilon differentiated with respect to time? (see my question on the right)
0
votes
0answers
70 views

Point source approximation

I have a 0.05 mm radius sperical source of Photons, and a 10 mm X 10 mm detector aligned to be orthogonal to their distance vector. Distance is D $\approx$ mm. I want to know how good the point ...
1
vote
0answers
193 views

Adiabatic approximation and time-dependent problems

I am an undergraduate physics student. I have a question in approximation methods for time-dependent problems in quantum mechanics. I read the proof of the adiabatic theorem but I didn't understand ...
1
vote
0answers
67 views

Can anyone outline the theory of plane wave Born approximation for direct nuclear reactions in detail?

Can anyone outline the theory of plane wave Born approximation for direct nuclear reactions in detail? Also What are the modification introduced in the distorted wave Born approximation? I was ...
2
votes
0answers
105 views

Limits of integration for the radial wave function of the Hydrogen atom in the WKB approximation

I am working a problem where we have to find the energy eigenvalues for the radial wave function of the hydrogen atom for $\ell=0$ using the WKB approximation. I am sure that I set up the integral ...
4
votes
1answer
122 views

Why can we not apply perturbation theory in Born-Oppenheimer approximation

In Weinberg's Lectures on Quantum Mechanics, he mentions Unfortunately, we cannot simply use first-order perturbation theory, with $T_{nuc}$ taken as the perturbation and the state vectors ...
1
vote
1answer
187 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
220 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
vote
1answer
339 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
217 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 ...
1
vote
1answer
210 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
495 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
181 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
71 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
242 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?
1
vote
1answer
447 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
vote
1answer
700 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
86 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
210 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 = ...
-3
votes
2answers
180 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 ...