In quantum mechanics Definition and 251 Threads

Homework Statement Hi, I'm trying to self-study quantum mechanics, with a special interest for the group-theoretical aspect of it. I found in the internet some lecture notes from Professor Woit that I fouund interesting, so I decided to use them as my guide. Unfortunately I'm now stuck at a...

What is Cn in quantum mechanics?

In quantum mechanics, the velocity field which governs phase space, takes the form \begin{equation} \boldsymbol{\mathcal{w}}=\begin{pmatrix}\partial_tx\\\partial_tp\end{pmatrix} =\frac{1}{W}\begin{pmatrix}J_x\\J_p\end{pmatrix}...

Homework Statement Homework EquationsThe Attempt at a Solution These are what i solved except (e), I have no idea how to solve (e).

Hello! I would really appreciate it if somebody could recommend to me any books on geometric phases especially on Berry's phase. Thanks!

Hey guys, Hope all is well. I'm trying to get my head round some of the Quantum Mechanics of spin. I fully understand why the Pauli equation acts on a two component spinor wavefunction, where I'm a little confused is why the Dirac equation then acts on a 4 component spinor...

I was reading Bransden's Quantum Mechanics 2nd edition, chapter 2 page 61. There,it says "It should be noted that since E =hv (v for nu), the absolute value of the frequency has no physical significance in Quantum mechanics..." Why is that? Isn't this a contradiction?

in an attempt to get a better understanding of what happens during a measurement i have constructed a gedanken-experiment with two photon interference that regardless of its outcome seems to contradict quantum mechanics in one way or another and i was hoping to get a clarification here where i...

Hi, Can anyone please explain the physical meaning of coherence(Quantum Mechanics). Thanks is advance

Hi all, I have been reading lots of materials regarding the classical and quantum mechanics. The first subject I read is Bohr model, in which it is assumed the electron is in circular motion around the nucleus on the so-called orbital. I think it is semi-classical. With this assumption, we...

Hello everyone, There's something I am not understanding in Hermitian operators. Could anyone explain why the momentum operator: px = -iħ∂/∂x is a Hermitian operator? Knowing that Hermitian operators is equal to their adjoints (A = A†), how come the complex conjugate of px (iħ∂/∂x) = px...

Hi all, I got a feeling that learning quantum mechanics is easy and hard. Most of time, it is easy to "accept" all the concepts given in the book by simply looking at their mathematical interpretation. But it is hard if you really take it serious to try to understand everything from the...

I am an undergraduate student in India doing my final year BS degree in Math. I am extremely interested in quantum mechanics and want to peruse quantum computation. What is the best possible course that I can take for my Masters? There appears to be a limited number of colleges that offer a...

In classical mechanics we use a 6n-dimensional phase space, itself a vector space, to describe the state of a given system at anyone point in time, with the evolution of the state of a system being described in terms of a trajectory through the corresponding phase space. However, in quantum...

Hey Everyone, Question about time reversibility. In considering the reversibility of a system over an interval of time, shouldn't it be put into consideration, that because all interactions were random, that if one were to somehow "go back in time" or reverse the process, that the initial...

In case of tunnel effect in quantum mechanics we often consider time independent Schroedinger equation with potential ##0##, when ##x<0## then some ##V_0## when ##0\leq x\leq a## and ##0## when ##x>a## so potential barrier problem. And energy of particle that we send to barrier is ##E<V_0##. In...

In my lecture notes, it says that ##\left\langle l \right| A_{nm} \left| \psi \right\rangle = \sum_{n,m} A_{nm} \left\langle m \right| \left|\psi \right\rangle \left\langle l \right| \left| n \right\rangle## ##=\sum_{n,m} A_{nm}\left\langle m \right| \left| \psi \right\rangle \delta_{ln}## ##=...

Suppose I have an operator A. Its average is <A> and the standard deviation $$\sigma=\sqrt {<A^2>-<A>^2} $$. I now want the standard error which is $$\sigma/\sqrt {n} $$. I wondered what n is in quantum mechanics ? The wsvefunction is supposed to describe a single particle so it should be 1 ...

Given a transformation ##U## such that ##|\psi'>=U|\psi>##, the invariance ##<\psi'|\psi'>=<\psi|\psi>## of the scalar product under the transformation ##U## means that ##U## is either linear and unitary, or antilinear and antiunitary. How do I prove this? ##<\psi'|\psi'>## ##= <U\psi|U\psi>##...

Hi, I am trying to familiarize myself with the quantum mechanical trace distance and hit a brick wall. Thus, I would appreciate your help with the matter! I am reading up on trace distance using Nielsen, Chunang - Quantum Computation and Quantum Information and Bengtsson, Zyczkowski - Geometry...

I am a beginner in quantum mechanics and I am confused about the operator ΔA defined to be ΔA Ξ A - <A>. Can someone please tell me how to interpret <A>? From what I can understand, <A> is the expectation value and is defined to be <Ψ|A|Ψ>. But that is just a scalar correct? How do subtract a...

I'm Indian and I've heard stuff that it is difficult to get into a good PhD program in the US/UK for string theory because the competition is more fierce than other fields. Furthermore,the likelihood for getting academic positions is even tougher(added to the fact that I'm from a different...

I have been recently introduced to QM and I am deeply interested in it. I have come to know that quantum cryptography, quantum computing, and quantum optics are the hot areas where research is going on. But I'm curious, is there theoretical research going on for understanding of the quantum...

Homework Statement The demonstration for the momentum operator in Quantum Mechanics goes something like this <v>=\frac{d}{dt}<x>=\frac{d}{dt} \int x \Psi^* \Psi dx and then one ends up with <p>=m<v>=\int \Psi^* (-i \hbar \frac{d}{dx}) Psi dx however, if you swap the congugates you get...

I'm reading this tutorial on instructables for implementing the classical double-slit experiment. I've also read this thread for information which contains a very nice answer from @BruceW but still not resolves my confusion about the "sizes". First of all I'd like to make a distinction between...

So, I am kind of learning QM on my own, and through my chemistry book. It doesn't explain any further than the shapes of orbitals, and I am wondering did anyone found out why is space in the orbitals between the clusters of probability blank.

Hey JO. The Hamiltonian is: H= \frac{p_{x}^{2}+p_{y}^{2}}{2m} In quantum Mechanics: \hat{H}=-\frac{\hbar^{2}}{2m}(\frac{\partial^{2}}{\partial x^{2}}+\frac{\partial^{2}}{\partial x^{2}}) In polar coordinates: \hat{H}=-\frac{\hbar^{2}}{2m}( \frac{\partial^{2}}{\partial r^{2}}+\frac{1}{r}...

I'm interested in quantum mechanics but I am not sure where to begin. I have a a good understanding of classical mechanics, but I don't know where to start in quantum mechanics. I seem to dive into subjects that are too complicated for me to understand at the moment. Where is a good starting...

So I understand that as the number of entangled particles increases, observable quantum mechanical properties decrease to the extent that the mass of particles collectively loses its wave-particle character and behaves classically. In other words, the particles' collective position-space...

Hi, We know the convergence of a series but what does it mean to say that "an operator converges or diverges"?

Homework Statement Prove that ## [L_a,L_b L_b] =0 ## using Einstein summation convention.Homework Equations [/B] ## (1) [L_a,L_b] = i \hbar \epsilon_{abc} L_c ## ## (2) \epsilon_{abc} \epsilon_{auv} = \delta_{bu} \delta_{cv}- \delta_{bv} \delta_{cu}## ## (3) \epsilon_{abc} = \epsilon_{bca}...

If you have some wave function of some particle, say... |¥> And you calculate the expectation value of momentum, say... <¥|p|¥> What ensures that that spatial integral is real valued? Separately, all the components of the integral are complex valued

In classical physics, the definition of a unit of measure involves a deterministic process (e.g. "the amount of force necessary to give a kilogram mass the acceleration of 1 meter per second square"). How are such units defined in Quantum Mechanics? ( Do we replace references to quantities...

Hey, I am going to write my bachelor's thesis on Entropy in a Quantum Mechanical Framework. My professor told me he would refer me to some literature. However it will take him some time. I would like to get started myself. Could you please refer me to papers, books, articles? I have already read...

Homework Statement In the absence of degeneracy, prove that a sufficient condition for the equation below (1), where \left|a'\right> is an eigenket of A, et al., is (2) or (3). Homework Equations \sum_{b'} \left<c'|b'\right>\left<b'|a'\right>\left<a'|b'\right>\left<b'|c'\right> = \sum_{b',b''}...

Hi all, I am taking Quantum Mechanics II this coming spring semester. However, I haven't taken Linear algebra yet but I don't want to take the class just because for some few topics. What linear algebra topics should I learn before the class? Thanks!

Given psi as function of x^2, and the potential energy as function of x, find the kinetic energy. My reasoning: KE=P^2/2m and use the momentum operator. My professor's reasoning: Calculate the hamiltonian operator and subtract the potential energy then divide by psi. Note: I talked to my...

I would imagine that there are different viewpoints of what a particle is in quantum mechanics. Is it possible to get a summary of what they are?

In classical mechanics potential is defined for conservative forces and dissipative forces such as friction don't have potential. In quantum mechanics, Schrödinger equation which includes a potential, deals with problems. How can one treat the dissipative forces in quantum mechanics?

Homework Statement Good morning or afternoon. My quantum physics teacher has given me a task: Given a neutron beam of mass 1.27*10^-27 kg and known energy E impacts on a lineal chain of atoms with a known distance between two of them l. A detector intercepts the wave diffracted an angle o. I...

In a QM course, I learn that an operator can be represented by basis vectors If the basis vector is complete, the following relation holds There exist coefficient Mij such that Sigma Mij |i > < j|. = I , |i> is the basis! and I is the identity matrix But isn't that in linear algebra We...

I am learning about the basic quantum mechanics I know that an operator ,call it M^, is generally a matrix And we also can be represent it b a matrix representation M, associated with certain basis |e> M^ = sigma ( Mij |e> <e|) I,j Where Mij is matrix element of M So now I wonder...

You've probably been asked a similar question countless times I presume but please just hear me out. I am currently in my junior year of undergraduate and majoring in physics. For some time now I have really loved doing physics and I enjoy it, mostly the theory. But is taking it further and...

Hello everyone, I'm a beginner in quantum mechanics and I've been curious to know the textbook of that problem

Hello In the usual Hibert-space formulation of quantum mechanics, to each physical system is attached a separable Hilbert Space (generally infine-dimentionnal) over complex field. A crucial ingrediant in the description of a physical system is the notion of state and evolution of state...

Hello everybody. I am looking for a good graduate text in quantum mechanics. I studied from Griffiths during my undergraduate career and I loathed it. I thought it was sloppy and poorly arranged. Currently I have the one by Gottfried and Yan, "Quantum Mechanics: Fundamentals." I like it. It...

Hi, there Today, a friend came to me and asked the following questions and they made me confused. If the source is strong, the light has to be considered as wave, and the double-slit interference (DSI) can be interpreted, and the conditions for the DSI is (1) same frequencies, (2) parallel...

Hi, there Today, a friend came to me and asked the following questions and they made me confused. If the source is strong, the light has to be considered as wave, and the double-slit interference (DSI) can be interpreted, and the conditions for the DSI is (1) same frequencies, (2) parallel...

Homework Statement Calculate the commutative [P2,Lx] Homework Equations P2=P2x+P2y+P2z [Py,Lx]=-iħPz [Pz,Lx]=iħPy [Px,Lx]=[Py,Ly]=[Pz,Lz]=0 The Attempt at a Solution [P2,Lx]=[P2x+P2y+P2z,Lx] =[P2x,Lx]+[P2y,Lx]+[P2z,Lx] =Px[Px,Lx]+[Px,Lx]Px+Py[Py,Lx]+[Py,Lx]Py+Pz[Pz,Lx]+[Pz,Lx]Pz...

suppose we consider the measurement operator A=diag(1,-1). Then the tensor product of A by itself is in components : A\otimes A=a_{ij}a_{kl}=c_{ijkl} giving c_{1111}=c_{2222}=1, c_{1122}=c_{2211}=-1 and all other component 0. to diagonalize a tensor of order 4, we write ...