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17
votes
1answer
452 views

How is the logarithmic correction to the entropy of a non extremal black hole derived?

I`ve just read, that for non extremal black holes, there exists a logarithmic (and other) correction(s) to the well known term proportional to the area of the horizon such that $S = \frac{A}{4G} + K ...
12
votes
1answer
442 views

Hawking Radiation as Tunneling

Firstly, I'm aware that Hawking radiation can be derived in the "normal" way using the Bogoliubov transformation. However, I was intrigued by the heuristic explanation in terms of tunneling. The ...
10
votes
3answers
434 views

Why are electrons treated classically in cyclotron measurements?

As I understand , systems having large angular momenta relative to the planck constant (limit of large quantum numbers, e.g. $J/\hbar \to \infty$), can be treated as classical systems. Now in the case ...
10
votes
1answer
303 views

Probability conservation in WKB tunneling

Suppose we have quantum mechanical plane waves of energy $E$ incident upon a one-dimensional potential barrier $V(x)$ with sloping sides. One can compare the WKB solutions in the three relevant ...
10
votes
1answer
637 views

Eikonal approximation in QFT

Does the eikonal approximation for calculating a scattering amplitude in QFT provide the exact result in the limit of $s\rightarrow\infty$ at finite $t=0$ ($s$ and $t$ are the usual Mandelstam ...
9
votes
3answers
2k views

How does one quantize the phase-space semiclassically?

Often, when people give talks about semiclassical theories they are very shady about how quantization actually works. Usually they start with talking about a partition of $\hbar$-cells then end up ...
8
votes
2answers
837 views

Semiclassical limit of Quantum Mechanics

I find myself often puzzled with the different definitions one gives to "semiclassical limits" in the context of quantum mechanics, in other words limits that eventually turn quantum mechanics into ...
8
votes
2answers
341 views

Is WKB really applicable for the ground state?

It seems that WKB is applicable for a given $E$ if and only if $\hbar$ is sufficiently small. Or in other words, WKB is applicable if and only if the quantum number is large enough. Is this ...
8
votes
1answer
178 views

Hawking radiation for closely orbiting black holes

Suppose we have two black holes of radius $R_b$ orbiting at a distance $R_r$. I believe semi-classical approximations describe correctly the case where $R_r$ is much larger than the average black body ...
7
votes
1answer
1k views

What is a 'turning point' in WKB and why does it fail at that point?

What is meant by a classical turning point in quantum mechanics and why does the WKB approximation fail at that point?
7
votes
2answers
178 views

Perturbation theory for a particle in a weak potential

I have a basic question about quantum mechanics, maybe it has a basic answer. Take a free particle in a quartic potential, $L=\frac{1}{2}\dot{x}^2-\lambda x^4$ This is massless $\phi^4$ theory in 0+...
7
votes
1answer
271 views

Simulating the evolution of a wavepacket through a crystal lattice

I am interested simulating the evolution of an electronic wave packet through a crystal lattice which does not exhibit perfect translational symmetry. Specifically, in the Hamiltonian below, the ...
7
votes
1answer
250 views

Beyond WKB approximation for energies

In the first term the energies are given by the Wentzel–Kramers–Brillouin (WKB) formula $$ \oint p dq = 2\pi \left( n+\frac{1}{2} \right) $$ However, can this formula be improved to include ...
7
votes
3answers
926 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 ...
7
votes
1answer
363 views

Why does a damped quantum harmonic oscillator have the same decay rate as the equivalent classical system?

$\newcommand{ket}[1]{|#1\rangle} \newcommand{bbraket}[3]{\langle #1 | #2 | #3 \rangle}$ Why does the decay rate for a damped quantum harmonic oscillator exactly match the classical limit? Background ...
6
votes
2answers
1k views

Bohr-van Leeuwen theorem and quantum mechanics

Preamble: If one considers an ideal gas of non interacting charged particles of charge $q$ in a uniform magnetic field $\mathbf{B} = \mathbf{\nabla} \wedge \mathbf{A}$, then the classical partition ...
6
votes
1answer
1k views

Bohr-Sommerfeld quantization from the WKB approximation

How can one prove the Bohr-Sommerfeld quantization formula $$ \oint p~dq ~=~2\pi n \hbar $$ from the WKB ansatz solution $$\Psi(x)~=~e^{iS(x)/ \hbar}$$ for the Schroedinger equation? With $S$ the ...
6
votes
0answers
165 views

Looking for modern results in semiclassical physics and relevant references

What are some important approximations, especially those that are state-of-the-art, used to approximate the many-body dynamics of atoms and molecules in the semiclassical regime? To be clear, I'm not ...
5
votes
1answer
289 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 ...
4
votes
2answers
348 views

Is Ehrenfest theorem equivalent to Bohr's Correspondence Principle?

Ehrenfest theorem is usually dubbed as the quantum mechanical equivalent of Newton's law and Griffiths states, in the first chapter of his textbook, that Ehrenfests theorem enables us to work with ...
4
votes
1answer
429 views

Classical (or semi-classical) interpretation of photoelectric effect?

This site says that "it has recently been proven that the photoelectric effect can be interpreted classically (or at least semi-classically) in non-particle, wavelike terms". Is anyone familiar with ...
4
votes
1answer
87 views

Lack of Maslov index in the path integral formalism

Introduction Consider Feynman's famous path integral formula \begin{equation} K(x_a,x_b) = \int \mathcal{D}[x(t)] \exp \left[ \frac{i}{\hbar} \int_{t_a}^{t_b} dt \, \mathcal{L}(x(t),\dot{x}(t),t) \...
4
votes
2answers
138 views

Quasiclassical QM for central fields

Let's have quasiclassical QM for central field $V(r)$. The Schroedinger equation for radial part of wavefunction $R_{n\ell}$ after substitution $u_{n\ell} = rR_{n\ell}$ takes the form $$ u_{n\ell}{''} ...
4
votes
1answer
60 views

Vacuum energy: black hole evaporation and cosmology - a discrepancy?

Black hole evaporation is a result of calculating the expectation value of the stress-energy tensor of the state of the vacuum in certain spacetimes and then making a plausibility argument as to the ...
4
votes
0answers
105 views

Spaans, “On Quantum Contributions to Black Hole Growth”

This paper was posted to arxiv a couple of weeks ago: http://arxiv.org/abs/1309.1067 From the abstract: The effects of Wheeler's quantum foam on black hole growth are explored from an ...
3
votes
1answer
231 views

Planck's constant and phase space in quantum mechanics

During my undergrad physics classes, I've come across several seemingly related phenomena dealing with $h$ and phase space in quantum mechanics. Let $T_x$ be a translation operator by $x$ in ...
3
votes
1answer
53 views

WKB Approximation on an linear + harmonic potential

I have a quick question: I have performed the WKB approximation to find the energies of bound states in symmetric potentials (Square, harmonic, ...). To do this I just find the "turning points" by ...
3
votes
1answer
743 views

Alkali atom in oscilating electromagnetic field

I am trying to calculate atom - light (EM field) interaction Hamiltonian, and the results I get seem to me rather unphysical - I get some nonzero matrix elements which should not be there. Please, can ...
3
votes
2answers
190 views

How can I use a magnet to lift a paperclip?

This question has been asked already, but no satisfying answer came up. All the answers seem to push the problem further, but do not explain clearly what is going on. I will reformulate it for a ...
3
votes
1answer
592 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) = ...
2
votes
2answers
101 views

Generalisation of a particle in QFT

In classical mechanics, we assumed a particle to have a definite momentum and a definite position. Afterwards, with Quantum mechanics, we gave up the concept of a time-dependend position and momentum, ...
2
votes
3answers
257 views

Semiclassical quantization of bouncing ball

Consider an elastically bouncing ball of mass $m$ and energy $E$. This has a triangular potential $$ V(x)~=~\left\{\begin{array}{ll} mgx & \text{if } x>0, \\ \infty & \text{if } x<0, \...
2
votes
2answers
115 views

Semiclassical approximation in Quantum Field Theory

I've recently stumbled upon a semiclassical approximation to quantum field theory that I've never heard of and have a hard time understanding. Consider the Hamiltonian, \begin{equation} H = \frac{c}{ ...
2
votes
1answer
127 views

Classical spin viewed as $SU(2)$

In which sense is the configuration variable of a classical spin $SU(2)$? I can view a classical spin as a unit vector in $\mathbb{S}^2$ (2-dim. sphere), but it seems it is really given by a matrix $U$...
2
votes
3answers
176 views

Gravitational wave contribution of the Hawking radiation from a black hole

Black holes are expected to radiate like a perfect black radiator at the Hawking temperature, which means that they'll emit all particles according to the relevant formulas one can derive using ...
2
votes
1answer
385 views

Classical mechanics from Quantum mechanics

I'm looking at a way to prove that one recovers, under ad hoc assumptions, classical mechanics from quantum theory. Usually, we can find in textbooks that the propagator $$K(x,x_0;t)=\langle x|e^{-i ...
2
votes
1answer
271 views

Bohr-Sommerfeld quantization for different potentials

Let's have Bohr-Sommerfeld quantization for one-dimensional case: $$ \int \limits_{a}^{b} p(x)dx ~=~ \pi \hbar (n + \nu ). $$ Here $p(x) = \sqrt{2m(E - U)}$, $a, b$ are turning points, and the area ...
2
votes
1answer
57 views

Ground state energy $ E_{0} $ and evaluation of physical energies

Given the lowest eigenvalue $E_0$ of an Schrödinguer operator, do the other energies $ E_{n} $ for $ n >0 $ depend strongly on the lowest eigenvalue of the system? I mean, if we somehow fixed the ...
2
votes
1answer
306 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 ($x_1<...
2
votes
2answers
356 views

Why does the Bohr-Sommerfeld quantization for give the exact energy-levels for a harmonic oscillator?

Why does the Bohr-Sommerfeld rule for quantization give the exact energy-levels for a simple harmonic oscillator?
2
votes
2answers
208 views

can we apply WKB method for curved space times

let be the Hamiltonian of a surface $ H= g_{a,b} p^{a}p^{b} $ (Einstein summation assumed) my question is if although the space time is curved then can we use the WKB approximation to get the quantum ...
2
votes
1answer
168 views

Feynman's derivation of the Schrödinger equation

I'm reading the following article: Feynman's derivation of the Schrödinger equation In this article, the autor claims that Feynman derivation of the Schrödinger equation was a key aspect of the ...
2
votes
0answers
24 views

Non-equilibrium electronic distribution in the time-relaxation approximation - Which is the boundary condition?

In Chapter 13 of Ashcroft-Mermin - "Solid State Physics", the following non equilibrium electronic phase-space distribution for the semiclassical electrons in a periodic crystal is derived: $$g(\...
2
votes
0answers
61 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
0answers
132 views

WKB expression for Dirac equation?

given the one dimensional Schroedinger equation $$ - \frac{\hbar ^{2}}{2m} \frac{d^{2}}{dx^{2}}\Psi(x)+ V(x) \Psi(x) =E_{n}\Psi (x) $$ the WKB method for the energies is $$ (n+1)2\pi \hbar =\int_{a}...
1
vote
2answers
146 views

What is the spectrum of energies for the potential $ a^{x} $?

Given a certain potential $ a^{x} $ with positive non-zero 'a' are there a discrete spectrum of energy state for the Schrodinger equation $$ \frac{- \hbar ^{2}}{2m} \frac{d^{2}}{dx^{2}}f(x)+a^{x}f(x)...
1
vote
1answer
107 views

Is Gravitational Red shift equal to $mgh$

Is gravitational shift - $\frac{gh}{c^2}$ (according to pound-rebka experiment) always equal to $PE=mgh$? because assume the gravitational pull, $g$, is equal to $1$ then we can say $g = 1$ similarly ...
1
vote
3answers
349 views

Why do we obtain classical physics by taking the limit of Planck's constant to zero?

Why if we specifically set Planck's constant equal to zero (the limit of it) do we sometimes get classical physics? I mean, what does it mean physically to set the constant equal to zero? Or to say it ...
1
vote
2answers
471 views

Complex Versus Real Wave Velocities in Quantum Mechanics

There's a fantastic quote in Schrodinger's second 1926 paper1 that apparently provides some motivation for the discrete energy levels (I think) that I'm having trouble interpreting: I would not ...
1
vote
2answers
322 views

Phase space derivation of quantum harmonic oscillator partition function

I would like to derive the partition function for the quantum Harmonic oscillator from scratch: $$\tag{1} Z = \int dp \, dx\, e^{-\beta H}.$$ The free particle appears in many textbooks. $H = p^2$...