Quantization Definition and 274 Threads

For the simple harmonic oscillator case, the energy is E=(n+1/2)hw, and N|n>=n|n>. It seems second quantization explain it as there are n bosons with each particle has energy homework plus vacuum 1/2hw. But we know before second quantization, there is only one particle with energy nhw plus...

Hi,all What is the motivation of using Second Quantization ? What kind of situation does people want to use field operators ? Euphemia

I have a technical question and at the time being I can't ask it to a professor. So, I'm here: If I try to quantize the vector field in the Coulomb gauge (radiation gauge) A_0(x)=0,\quad \vec\nabla\cdot\vec A=0. by imposing the equal-time commutation relation...

I don't know what the speed of light c is doing in the Hamiltonian for the Landau quantization. The term doesn't have dimensions of momentum anymore. :confused: \hat{H}=\dfrac{\hat{p}^2_x}{2m}+\dfrac{1}{2m}\left(\hat{p}_y-\dfrac{q|\vec{B}|}{c}\hat{x}\right)^2 Any ideas? thanks.

I wonder what happens if you have trapped hydrogen atoms and you apply a magnetic field. We could observe the Zeeman effect; some electrons would gain energy and some other would lose energy due to the magnetic field. Say an electron gained some energy. Now you remove the magnetic field, the...

Homework Statement This problem involves an electric monopole placed at the origin and a magnetic monopole placed a distance D away, say arbitrarily, along the z-axis. I need to compute the angular momentum of the EM fieds: \vec{J_{field}} = \frac{1}{4\pi c}\int{d\tau \vec{r} \times...

Instead of quantizing the vector potential A^μ why we do not directly quantize the B and E fields in electrodynamics.

Is it true that in first quantization the PI includes the possible trajectories a particle can take, but it does not include how particles can change into other kinds of particles (electrons to photons, etc). And QFT (second quantization) calculates how particles can branch off into other...

Homework Statement I don't understand what E = nhv means. What does it apply to and what does the n (energy level) mean in the equation. It says in the textbook, "According to Planck, the atoms of the solid osscillate with a definite frequency depending on the solid. But in order to...

If space-time itself is quantified, and the spatial universe has, at anyone time, a finite volume, would this not imply that at anyone moment there are a finite number of spatial locations? (If so, then integrating over an infinite number of points would only give an approximation.)

"Black Hole Masses are Quantized," Gia Dvali, Cesar Gomez, Slava Mukhanov, http://arxiv.org/abs/1106.5894 There is a nontechnical summary on the arxiv blog: http://www.technologyreview.com/blog/arxiv/ , along with some inflammatory and uninformed speculation about safety at the LHC, including...

I'm not quite sure which forum I should post this in; it's related to my school work but I don't have any homework questions about it. Rather, I am just confused about what it really is and what it means. Hopefully it goes here. I get that the projection of the angular momentum along some...

I'm wondering if the potential term in the Lagrangian for a single particle is just an approximate way to summarize all the interactions of virtual particles created by the potential at every point. For example, the EM field is mediated by photons at every point in space. In reality an electron...

Please teach me this: When calculating something with Grassman numbers without changing order of the numbers,then there are nothing different from ordinary numbers.So I think it would be contrary if we define the complex conjugation of a product of two Grassman numbers to reverse the order of...

I'd like to focus in on some info from a previous thread that seemed too good to pass up https://www.physicsforums.com/showthread.php?p=3156965 Yes I was making that confusion, and I'd like to understand this a bit better. I have three questions to follow up if you don't mind. Is there a...

I begin with \int (\bar{\psi}(x) (\mathcal{H} \psi(x)) d^3x This is just \int (\bar{\psi}(x) ({\frac{p^2}{2M} + \frac{1}{2}M \omega^2 (x)} \psi(x)) d^3x If one identified that \bar{\psi}(x) and \psi(x) are creation and annihilation operators, I assume that I can simply restate my...

If you look up the second quantization spin operator, you'll notice that there are two indices on the pauli vector for two possible spins. The operator sums over these two indices. Since the pauli vector is an unchanging quantity what do these indices physically correspond to?

Hi Say I have the following two fermionic creation/annihilation operators c^\dagger_ic_j 1) Yesterday, my lecturer said that the following is valid c^\dagger_ic_j = \delta_{i,j}c_jc^\dagger_i Can you guys explain to me, where this formula comes from? I originally thought that it was one...

Hi. I've been trying to calculate a couple of commutators, namely [\Psi(r),H] and [\Psi^{\dagger}(r),H] where H is a free particle hamiltonian in second quantization. I have attached my attempts and I would greatly appreciate if anyone could tell me if I am right or if there is a better way to...

Didnt seem to be many threads about this subject although I don't find it trivial at all.. Lets start with a question: If we now have <N_i - 1|â_i|N_i> = N_i^0.5 but let â operate on our ket it should give: <N_i - 1||N_i - 1> = N_i^0.5 its adjoint however is the creation operator (right?)...

I was reading the book written by Peskin about QFT when I found that the following equation: (\frac{\partial}{\partial t^2}}+p^2+m^2)\phi(\vector{p},t)=0 has as solutions the solutions of an Harmonic Oscillator. From what I know about harmonic oscillators, the equation describing them should...

Hi I have a question regarding second quantization. In the following link...

1. The problem statement Problem: "Consider a classical particle with charge q and mass m in 2 dimensions (xy-plane) moving in the presence of a uniform magnetic field B=B_z.'' There are a number of parts to this problem, but it's the first three that have me confused. "(a) Describe the...

Hi. I'm reading an article which writes the following "... and the well-known expression for the charge current is" j=-\frac{ie}{m}\int dr\psi^\dagger (r)[\nabla-ieA(r)]\psi(r) Why does it have an integral sign? And when you define it this way, you integrate out the r-dependence...

Homework Statement how does Planck's idea of quantization of the energy found in electromagnetic waves solve the problem of black body radiation? Homework Equations N/A The Attempt at a Solution this is what i have said correct me if I am wrong... so plank said that photon has...

How do I express an arbitrary 2-particle state in second quantization? I could write this |\psi\rangle=\sum_{mn}c_{mn} a_m^\dagger a_n^\dagger |0\rangle where c_{mn} is a constant, a_n^\dagger is the creation operator and |0\rangle is the vacuum state. The only problem is that I want to...

I have a question regarding quantization. In most cases one never starts with a quantum theory, but always writes down a classical expression, goes through quantization, implementation of constraints (Dirac, BRST, ...), construction of Hilbert space, inner product, measure of an path integral...

A new quantization method for relativistic fields has been recently proposed. Compact time naturally reproduces canonical quantum mechanics as well as the path integral formulation, and in a deterministic way (no hidden-variables)! It seems to be a new way of thinking to the concept of time...

Homework Statement Q1 A linear PCM system has an input signal 2cos6000PIt volt. Determine, (a) the minimum sampling rate required, (b) the number of bits per PCM codeword required for a signal to quantization noise ratio of at least 40 dB, (c) the maximum quantization error voltage, (d)...

Hi, for my exam i"m re-reading Peskin&Schroeder and stumbled across equations 2.21-2.25 where the canonical quantization of the KG field is done. P&S start with doing a Fourier trf on \phi(x,t)=\int\frac{d^3p}{(2\pi)^3}e^{ip\cdot x}\phi(p,t) applying the KG operator in that results in...

Hi guys The fermionic creating and annihiliations operators: Do they satisfy c_{i,\sigma }^\dag c_{i,\sigma }^{} = - c_{i,\sigma }^{} c_{i,\sigma }^\dag for some quantum number i and spin σ, i.e. do they commute?

Hey folks, i have a question concerning canonical and path integral quantization. From what I have understood so far, these two techniques are different and independent but equivalent. My problem is that I don't really see where the quantum character enters in the path intregral formulation...

1. The most probable point a 1s electron will be found in the hydrogen atom is r = 0. 2. The most probable distance that a 1s electron will be found in the hydrogen atom is r = 0. 3. For a hydrogen atom with l (lower case L) = 0, Ψ is independent of the angles Θ and Φ. 4. For a hydrogen atom...

I'm being asked on a homework to show that the m orbital angular momentum quantum number can only take integer values. Using ladder operators I know how to prove that m is restricted to half-integers, but I'm having trouble with a further restriction. I'm quite certain the problem does not want...

Hi guys When working with operators in second quantization, I always imagine c^\dagger_ic_j as denoting the "good old" matrix element \left\langle {i} \mathrel{\left | {\vphantom {i j}} \right. \kern-\nulldelimiterspace} {j} \right\rangle . But how should I interpret an...

http://arxiv.org/abs/1004.2260 The new vertices and canonical quantization Sergei Alexandrov (Submitted on 13 Apr 2010) We present two results on the recently proposed new spin foam models. First, we show how a (slightly modified) restriction on representations in the EPRL model leads to...

This commmunity has so many nice people, so helpful, I am learning QFT from Srednicki I would be glad if some one can clarify, all the books talk about boundary conditions which are finite at spatial infinity and give the general solution for canonical quantization of scalar field, 1) how...

I'd like to ask one 'newbie' question on the quantization of the E/M field. I know that when we quantize the E/M field we get infinite in number harmonic oscillators. I just want to know, what's the 'physical meaning' of these harmonic oscillators? How do we interpret this result...

Hi guys Today my lecturer talked about second quantization, and at the end he talked about free fermions in second quantization. He said that free electrons in second quantization satisfy that their Hamiltonian is only written as a linear combination in terms of c^\dagger c (the creation and...

I am trying to learn the integer quantum hall effect and have a pretty straightforward question. I understand that the normal translation group does not commute with the Landau Hamiltonian. Does this mean that if you have a state in the lowest Landau level (LLL) and apply the translation...

Hi all I am reading about second quantization. The kinetic energy operator T we write as \hat T = \sum\limits_{i,j} {\left\langle i \right|T\left| j \right\rangle } \,c_i^\dag c_j^{}. Now, the creation and annihilation operators really seem to be analogous (in some sense) to the...

Hi, I have recently been reading Dirac's book on Canonical Quantization of gauge theories, and I have a few questions: So in the quantization procedure we need to identify all the constraints in the theory. Once this has been done (if we are dealing with a gauge theory) we need to check...

[b]1. The allowable radius of spinning electron in uniform magnetic field using sommerfield quantization condition [b]3. Subs mv/r=qvB and some of its variation (like th period 2pi*r /v) into the closed int of pdq=nh and I got r=sqr((nh)/(2pi*qB)). Is this correct. I can't find anything about...

I'm reviewing my undergraduate quantum mechanics from a while back, and I am not quite sure I understand this correctly. I seem to recall being taught that quantization arises from the imposition of boundary conditions (in the mathematical sense). But this isn't quite the same as saying that...

Hello, I'm struggling with the second quantization formalism. I'd like to derive the hamiltonian of a system with non-interacting particles \hat{H}=\int dx\,a(x)^\dagger \left[\frac{\hat{P}}{2m}+V(x)\right]a(x), where a(x) = \hat{\Psi}(x). I know the second quantized representation of a...

Homework Statement My textbook indicates the following three important points are confirmed by Faraday's law of electolysis: a) matter consists of molecules and molecules consist of atoms b) charge is quantized; only integral numbers of charges are transferred to the electrodes c)...

Hi. In second quantization (not QFT or anything advanced like that) we have the particle density \hat n(x)=\Psi^{\dagger}(x)\Psi(x) using the usual field creation/annihilation operators. For a single particle we obtain for the expectation value in the state |\psi\rangle: \langle \psi |...

Does anybody know about an attempt to quantize teleparallel gravity? I would like to learn more about it, canonical approaches preferred: is there a sound formalism to implement the constraints / symmetries? Do we know the physical Hilbert space? Can one construct Dirac observables? Does the...

I have just come to learn (Physics, with modern physics, Richard Wolfson, J M. Pasachoff, second edition) that not only angular momentum's magnitude is quantized, but also its direction. Its given that, Cos\thetamin= l / \sqrt{l(l+1)} Telling that, \thetamin is the minimum angle between any...

I'm learning about Schrodinger's equation in my general chem class right now, so obviously I'm doing a little background reading on quantum theory. The following is an excerpt from a supplement on basic (very basic) quantum theory: The answer is that quantization is only noticeable when...