Quantization Definition and 274 Threads

Hi everyone, I'm reading section 9.2 of Peskin and Schroeder, and have trouble understanding the origin of a term in the transition from equation 9.26 to 9.27. Specifically, equation 9.26 is \frac{1}{V^2}\sum_{m,l}e^{-(k_m\cdot x_1 + k_l\cdot x_2)}\left(\prod_{k_{n}^{0}>0}\int d \Re...

In coordinate representation in QM probality density is: \rho(\vec{r})=\psi^*(\vec{r})\psi(\vec{r}) in RSQ representation operator of density of particles is \hat{n}(\vec{r})=\hat{\psi}^{\dagger}(\vec{r})\hat{\psi}(\vec{r}) Is this some relation between this operator and density...

Homework Statement A simple pendulum has a length equal to 0.6 m and has a bob that has a mass equal to 0.5 kg. The energy of this oscillator is quantized, and the allowed values of energy are given by En = (n + 1/2)hf0, where n is an integer and f0 is the frequency of the pendulum. Find n if...

Dear all, Since standard QM textbook Sakurai or Shankar only mention Non-relativistic path integral and QFT text deal with path integral for field theory, I want to ask whether there is a subject like "Path Intergral quantization for Relativistic point like Particles"? If so, is this subject...

in schrodinger equation(time independent) d^2y/dx2= 2m/h^2(V-E)y, V is a function of position coordinate, y is eigenfunction. if E>V , y being -ve or +ve it would be a oscillatory function. The allowed energy values are continously distributed...

Homework Statement (from "Advanced Quantum Mechanics", by Franz Schwabl) Show, by verifying the relation \[n(\bold{x})|\phi\rangle = \delta(\bold{x}-\bold{x'})|\phi\rangle\], that the state \[|\phi\rangle = \psi^\dagger(\bold{x'})|0\rangle\] (\[|0\rangle =\]vacuum state) describes a...

Bohr's second postulate says that it is only possible for an electron to move in an orbit for which its orbital angular momentum L is an integral multiple of \hbar. Can somebody please derive and explain L= n\hbar for me? I feel like a total dummy for not understanding this, but this is what I...

Are photon wavelengths quantizised? If so, what are their possible wavelengths? Do their possible wavelengths also depend on the system they are in?

How should I understand the procedure of canonical quantization in quantum field theory. Do we really quantize the field by regarding the field as dynamics variables ?What’s the physical essence of quantization?

Now this might seem to be a very stupid question. But neverthless, I don't understand why the fundamental quantization of energy must be hv? why not any value lower or higher like hv^2 or h/v^2. Is it possible to prove that this value of quantization is most favourable than any other value...

hi there we know that electrons around the nucleus in an atom can only exist in certain discrete energy levels (orbits) and that they can jump from one energy state to a higher one or a lower one. where is the electron when it is jumping from a higher stste to a lower state if it cannot exist...

Hi! Is there a common way to write a fermionic Fock space (finite dimensional) as a tensor product such that it is possible to do a partial trace over one particle type? Sorry, if this is an obvious question, but I just can't see it. Thanks!

I have a question about spacetime...if spacetime was quantized, would we still be considered to have 3 spatial dimensions? As far as I understand, 3 numbers are the minimum that we currently need to specify a location somewhere in space after selecting an arbitrary origin (the numbers are...

Here are the talks planned for this month's BH-LQG workshop. I think one thing that motivated the organizers is the recent appearance of results showing a step-wise increase in BH entropy. That is the increase is only approximately linear with horizon area---detailed analysis shows more...

in diffeomorphism invariant theory, which is the meaning of the time in quantization? or in other words which is the right time for quantization?

My professor mentioned that the pauli exclusion principle applies to the nucleus. How exactly is the nucleus quantized (the protons and neutrons), and how do the quantization rules apply to it (such as pauli's, hunds, and so on). Also, is this the reason why we don't observed multiple neutrons...

http://arxiv.org/PS_cache/arxiv/pdf/0712/0712.3833v2.pdf Fourier spectral analysis has been carried out on the quasar number count as a function of redshift calculated from the quasar data of the Sloan Digital Sky Survey DR6 data release. The results indicate that quasars have preferred...

I am searching material in second quantization in ashtekar-like formulation gravity. Somebody knows something like that? thanks

bohr model: permitted radii? Homework Statement A new (fifth) force has been proposed that binds an object to a central body through a potential energy function given by: U(r) = -Dr^{\frac{-3}{2}} 2 r > 0 and D > 0 (a) What is the (central) force F(r) associated with this potential...

Why the quantization of scalar field resolves the energy negative problem that exist in the klein-gordon equation?

For example, I want to know how to quantize a free particle in the spherical coordinates. Given a classical Hamiltonian H(r, \theta, \phi, p_r, p_{\theta}, p_{\phi}), the standard procedure tells us to let r, \theta, \phi be operators and they form a complete set. And The corresponding...

Is there any paper on the quantization of color? Maybe not since it’s obvious. I always thought that color was on a continuum. But now I realize that electrons jump between a limited set of orbits.

Quantum Wave Cosmology is a niche in cosmology that consists of a group of “not easily refuted” protoscience ideas about a universe composed of nothing but energy. A few QWC ideas include: The universe is composed of one commodity, energy. Energy cannot be created or destroyed and so...

Hi all, I am looking at (elementary) theory of superconductivity. In particular, I am looking at the calculation showing that a (however small) attractive interaction makes the Fermi sea unstable. Kittel's "Introduction to solid state physics" (7 ed) sketches this calculation in Appendix...

Is the 2nd quantization physically essential in the description of relativistic fermions obeying Dirac equation? In the case of the non-relativistic Schrodinger equation, the 2nd quantization is only a matter of convenience and doesn't actually change any physics, for both bosons and...

let be the Lagrangian (1/2)m( \dot x ^{2} + \dot y^{2}) - \lambda (x^{2}+y^{2}-R^{2}) with 'lambda' a Lagrange multiplier , and 'R' is the radius of an sphere. basically , this would be the movement of a particle in 2-d with the constraint that the particle must move on an sphere of...

I'm a bit embarrased to ask this (thats why I'm asking here and not asking one of my professors), as a grad student in Physics I've had a good deal of quantum mechanics, but one thing I haven't fully understood yet is the mechanism in the Schrodinger Equation that forces eigenvalue quantization...

Quantization of Gauge theories ?? Hi , i am trying to learn the math formalism of Gauge Theories as far as i know they begin with the 1-form A= \sum_{i} T^{i}A_{\mu}^{i} where 'T_i ' are the generators of the Lie Group then we define the 2-form F= dA + (1/2)[A,A] and the...

I don't have the Zwiebach's string theory book myself, but I paid a visit to a library, and took a glance on it. The chapter 5 was about relativistic point particle. Now, did I understand correctly, that the string people actually have a technique to quantize a relativistic point particle? I...

So this is sort of a belated response to some comments that were made in here over the last couple weeks and that I've been thinking about since. In the thread about the Lisi article in the New Yorker, Mtd2 and Kea were asking Garrett about whether he is still using a "superconnection" and...

In the Anderson model, it cost an energy Un_{\Uparrow}n_{\Downarrow} for a quantum dot level to be occupied by two electrons. Here n_{\Uparrow} is the second quantized number operator, counting the number of particles with spin \Uparrow. I need the term Un_{\Uparrow}n_{\Downarrow} in first...

Let's have a theory involving Dirac field \psi. This theory is decribed by some Lagrangian density \mathcal{L}(\psi,\partial_\mu\psi). Taking \psi as the canonical dynamical variable, its conjugate momentum is defined as \pi=\frac{\partial\mathcal{L}}{\partial(\partial_0\psi)} Than the...

So I actually decided to make an effort to study for my quantum final ahead of time, and I'm trying to find books that cover second quantization. If possible I'd like to find a book that gives a decent explanation (with examples, maybe?) of the Bogoliubov transformation. Does anyone have any...

I have read that when the rate in change in flux wrt time=0 the current become constant and the flux get trapped in the superconductor loop but how does this flux quantization exist exactly and under which rules it exist? and i want to ask is there something called voltage quantization?! and if...

Suppose I have a system of N identical bosons interacting via pairwise potential V(\vec{x} - \vec{x}'). I want to show that the expectation of the Hamiltonian in the non-interacting ground state is \frac{N(N-1)}{2\mathcal{V}}\widetilde{V}(0) where \widetilde{V}(q) = \int d^3 \vec{x}...

When defining a field operator, textbooks usually say that one can define an operator which destroys (or creates) a particle at position r. What does this really mean? Are they actually referring to destroying (or creating) a state who has specific quantum numbers associated with the geometry...

Pretty basic question: If energy levels (say, of an electron) are quantized, how is an interaction resolved wherein incoming energy (say, a photon) is not of an appropriate amount of energy to result in an appropriate response (say, moving from 1s to 2s in a simple hydrogen atom)? Suppose the...

The values of theta that represent the angle b/w orbital quantum no. (l) & magnetic field direction can never by pi or 0 deg as then the magnetic quantum no . will have non integral values & and also the direction of orbital quantum no . & magnetic field will be parallel which means the electron...

Use the Bohr quantization rules to calculate the energy levels for a harmonic oscillator, for which the energy is p²/2m + mw²r²/2; that is, the force is mw²r, where w is the classical angular freq of the oscillator. Restrict yourself to circular orbits. So far I have that mvr=nh\, w=v/r, and...

Quantization and fluid mechanics?? Cant quantum field theory be applied to releativistic imcompressible fluids? cant the velocity vector field be quantized? will the pressure of the fluid play the role of the 4th component of the four vector? what would be the corresponding quanta? (I know...

Mass Quantization! Homework Statement Elementary particles seem to have a discrete set of rest masses.Can this be regarded as quantization of mass? Homework Equations The Attempt at a Solution No,the rest masses are not found to be integral multiple of some fundamental mass unit...

i understand that adding heat to an atom will cause the electrons to populate higher energy levels... but apparently doing work will cause the energy levels themselves to change (increase i guess?) Is this true and if so why?! Thanks!

Photon Question-Energy Quantization Question---please help! This is a somewhat simple question I'm just unsure what relations to use. I found an equation relating number of protons to power and frequency but I'm not sure how to apply it to this case. EQUATION? Power = energy per unit time...

When quantizing a static force field, say a Coulomb field, we get off mass shell, virtual particles and we say they transmit the force between two charges. They say the exchange of particles produces a force. It's a very profound and important concept in physics. But then, as I read many...

Write momentum, kinetic and potential energy, and two particle interaction in second quantization. That is the question that I need to answer for my exam, but I don't have any idea what second quantization is, except that you can solve harmonic oscilator by using ladder operators. I can't find...

acceleration quantization ?? If x \Psi (x,t)=x \Psi(x,t) and p \Psi (x,t)= -i\hbar \partial _{x} \Psi (x,t) then should it be a \Psi (x,t) = \dot p \Psi (x,t)= \hbar ^{2} \partial _{xt} \Psi (x,t) using usual QM So, the direct quantization of motion equation (constraint) should...

Can we apply 'Quantization' only from motion equation ?? Supposing you have the equation of motion (in terms of momenta and position) F(\dot p_{a} , q_{a})=0 then can you obtain the 'Quantum analogue' without the intervention of the Lagrangian ? and another question could we regard...

The “math kids” are hard at work. http://arxiv.org/PS_cache/arxiv/pdf/0705/0705.3892v1.pdf Spin foam model from canonical quantization Sergei Alexandrov 26 may 2007 ----------- A quick search of dual 4-simplex found this supplementary information...

If I accelerate a charge, EM radiation is emitted. For a simple dipole model, the radiation propagates outward along a torus shape (see Griffiths, Intro to ED, 3ed., fig 11.4) - the acceleration field, with power according to Larmor formula. Since EMR is quantized, in what way is the described...

I am obtaining data with a sample rate of 6250 samples/second on a digital oscilloscope. Ideally, I am obtaining a sinusoid output through a system from a sinusoid input. My expected results through the system are lower in amplitude than I am actually recording. I have some reasons for why...