Qm Definition and 1000 Threads

I'm not posing this to be a forum troll or to insult the excellent ongoing work in Physics. It's a serious question based on the following: * Most of relativity and QM theory was completed within 20 years by a few dozen scientists. * Their tools were very primitive-not even electric...

In a popular book on quantum gravity "Physics meets Philo on the Planck Scale", it is mentioned there are 4 roads to quantum gravity: "1. quantising General Relativity 2. quantising a different classical theory, while still having general relativity emerge as a low- energy (large-distance)...

Hi all I am trying to go through the Griffiths Intro to QM book and I'm afraid I'm already stumped! He determines the momentum operator by beginning with the following equation: <x>=\int_{-\infty}^\infty {x|\psi(x)|^2} He takes the time derivative and manipulates the integral: (I'm...

Homework Statement An electron is confined to a 1 dimensional infinite well 0 \leq x \leq L Use lowest order pertubation theory to determine the shift in the second level due to a pertubation V(x) = -V_0 \frac{x}{L} where Vo is small (0.1eV). Homework Equations [1] E_n \approx...

Homework Statement V(x) = 0 if \frac{-L}{2}<x<\frac{L}{2} and \infty otherwise. Is the wave function \Psi = (2/L)^{1/2} (sin (\pix/L) an acceptable solution to this? Explain Homework Equations H\Psi= E\Psi , normalization: 1 = \int wavefunction^{2}dx The Attempt at a Solution...

Homework Statement Write down the time independant Schrodinger eqn in the momentum representation for a particle with mass m when the potential is given by V(x) = \frac{1}{2} \gamma x^2 Given that a possible solution is given by \Phi(p) = e^{\frac{-Bp^2}{2}} determine B and the...

I've done this experiment several times, and once upon a time I could describe exactly what is shown - but that was a while ago. I need a refresher. Take two polarizing lenses (let's keep it simple - transverse polarization), lens A and B, turn them 90 degrees to each other, they will block all...

Hello! I just finished my undergraduate quantum mechanics education and am looking to self-study the next level some time soon (after finals!). We used Gasiorowicz in my class: a god-awful pedagogical text in my opinion. Though I've done pretty well in my course (I'm fairly certain I have...

Hi On Wikipedia some author wrote: According to Quantum Mechanics, particles can't inhabit a place smaller than their wavelength. I googled around a little bit but couldn't find any formula which is consistent with this sentence. Anybody knows by which formula this sentence makes sense...

In classical mechanics, I can measure the inertial mass of a particle by measuring force and acceleration: m=F/a. In QM, this equation only holds for expectation values <F> and <a>. Does this lead to the fact that inertial mass is not an observable? Is there a deeper underlying principle which...

Homework Statement I'll try to recreate from my memory the problem we've been assigned on a test more than one month ago. They gave the solution but I either misunderstood or miscopied it. An electron with kinetic energy 5 eV goes from a region with potential V_0=6 eV (let's call this region...

Hi, I have a BS in Physics and Math, and am taking a 2 year hiatus to bike to Argentina. I'm currently 3000 miles in, 14000 left. Anyway, I am going to apply to graduate school for admission 2013, and I'm interested in theoretical physics. Primarily, I am interested in the foundations of...

I want to understand positive operator valued measures in QM, in particular why they are considered "observables". Anyone know a good place to start reading about this? I know some functional analysis and some measure theory, but I haven't made it all the way to the spectral theorem.

Homework Statement The potential of a simple harmonic oscillator of HF has the following form \frac{1}{2}kx^2 + bx^3 + cx^4 The first part of the problem involved finding expressions for the first-order energy corrections for the first three states, which I found below. Basically the x3 term...

Homework Statement Concicer the dilation operator D = \vec{r} * \vec{p} Compute [D,\vec{r} ] and [D, \vec{p}] Homework Equations p = - i * hbar The Attempt at a Solution I think the question is really if [D, \vec{r}] commutes I got this: D = \vec{r} * \vec{p}...

What is the definition of "particle(s)" in QM? Hello, It is said that "identical particles are indistinguishable", but I'm beginning to think such a weird sentence is only a result of butchering the word "particle". More concretely: what is actually meant with the word "particle" in the QM...

Homework Statement Okay so I've got a question I really need answered first up! If I have a 2x1 matrix for Psi, is Psi* a 1x2 matrix with all the 'i's turned to '-i's? Now onto the actual question - http://imgur.com/3ucb4" - part b only Homework Equations http://imgur.com/bcEm3"...

Can you make a definition of velocity in QM ? I am trying to find a general definition of velocity in QM. QM is totally different world !

A footnote to Griffiths reads "In a deep sense all of the mysteries of quantum mechanics can be traced to the fact that position and momentum do not commute. Indeed, some authors take the canonical commutation relation as an axiom of the theory, and use it to derive [itex]p = (\hbar /...

Hi, I'm looking for a book that presents a pragmatic interpretation of QM that'd be appropriate for someone who's taken one semester of it.

On page 96, he defined \psi'(x')=S\psi(x), but it seems what he later derived for S only transforms the spinor part not the space-time coordinate of the 4-component wave function, then how is the space-time coordinate primed after acted by S? I'm pretty sure it's not a typo according to what he...

Hello All, Right now, I am trying to complete my QM assignment, but I am getting confused about the notation. So, the generalized angular momentum operator is represented as \hat{J} and -j is the quantum # associated with the magnitude and m_{j} is the quantum # associated with the...

I have read similar threads about this problem but I wasn't able to make progress using them. Homework Statement Consider an infinite square-well potential of width a, but with the coordinate system shifted so that the infinite potential barriers lie at x=\frac{-a}{2} and x=\frac{a}{2}...

I have this review question: If operators A and B are hermitian, prove that their commutator is "anti-hermitian", ie) [A,B]†=-[A,B] What has me confused is the placement of the dagger on the commutator. Why [A,B]† and not [A†,B†]? Also, I am using Griffith's Intro to QM as a text. I have...

Hi Guys I have recently been reacquainting myself with Ballantines - Quantum Mechanics - A Modern Development. He is pretty big on the Ensemble interpretation, and I must admit I am rather attracted to it as well - none of this collapse of a wave function stuff, many worlds etc. He also makes...

This isn't a HW problem, it's more of a general question. I'm reading Griffith's Intro to QM 3rd Edition. On page 134 he uses separation of variables, of which I'm familiar (but by no means an expert). Could someone explain why the separation constant in equations 4.16 and 4.17 changes sign...

Studying in the Heisenberg picture, we have \frac{\text{d}x_i}{\text{d}t}=-\frac{\text{i}}{\hbar}[x_i,H]=\frac{1}{m}\left(p_i-\frac{q}{c}A_i\right) where the last bracket is known as the kinematic momentum \pi . Now, to find \frac{\text{d}^2{\bf{x}}}{\text{d}t^2} I do the following...

I am starting to become confused when reading about quantum mechanics and its treatment of photons. I heard somewhere (I can't recall where) that the characteristic intensity of a photon beam was give by I = E/\omega, where \omega is the angular frequency of the beam. However, I can't seem to...

Is anyone in PF reading the titled book? For me, it is slow work because I have not done physics for a while - decades! I am retired and read some old physics books just for challenge. Mueller gives me that, but also reward. From time to time, I find little stumbling blocks, sometimes a...

Hello :smile: I think my question is clear... Another questions that need to be asked: What about the deterministic interpretations of QM? and Do indeterministic interpretations PROVE that there is really no causality on subatomic level ? Please help me! I am more than a little confused...

How are internal lines with no free ends of Feynman diagrams of the perturbative expansion of QFT related to the quantum tunnelling barrier's negative kinetic energy and the HUP of QM? (if they are related at all)

I'm an undergrad currently taking my first course in QM. We've just about finished our chapters on the mathematical formalism and it has been making me pose a lot of questions. We use a lot of vocabulary/definitions that I suspect come from higher algebra, topology, & functional analysis all...

Can someone list some of the phenomena only explicable via QM?

Problem10.1, Introductory QM,Liboff. Homework Statement If \psi (\mathbf{r},t) is a free-particle state and b(\mathbf{k},t) the momentum probability amplitude for this same state, show that \iiint \psi^* \psi d \mathbf{r}=\iiint b^* b d \mathbf{k} Homework Equations \psi_\mathbf{k}...

QM-- Stefan's constant vs radiation constant Homework Statement (a) Using Planck's formula for the energy density ρ(λ,T), prove that the total energy density is given by ρ(T)=aT4 where a = 8π5k4/(15h3c3). (b) Does this agree with the Stefan-Boltzmann law for the total emissive power? The...

Homework Statement Find [Lz, Px] and [Lz,Py] and use this to show that \langle l'm'|P_x|lm\rangle = 0 for m' \neq m \pm 1. Homework Equations L_z|lm\rangle = \hbar m |lm\rangle L^2|lm\rangle = \hbar^2 l(l+1)|lm\rangle L_{\pm}|lm\rangle = \hbar \sqrt{l(l+1)-m(m\pm 1)}|l,m\pm 1 \rangle...

Hi, I have now finished University where I took an advanced quantum mechanics module in my final undergraduate year. Having left I was quite surprised to find out that this is infact only a grounding in the subject and I would like to know more. I have covered operators and the Hamiltonian...

I am an entering college freshman and i have a few questions about the uncertainty principle and hope my misunderstanding can be cleared up. Below is my horrible understanding thus far since my technical abilities are much below necessary for understanding qm, although it is too interesting a...

I've been looking for a good QM book for a while, and I'm considering purchasing Morrison's book. I've already completed an undergrad QM course with Griffith's. I would like to find a book that is strongly oriented towards relating QM theory to the real world, rather than just explaining how to...

Hi, In QM, when we make a measurement, our wavefunction collapses into one of the eigenstates of the operator. This process is supposed to be random for any single measurement but obeys some statistics if we make a large number of measurements. Could someone explain how we know that it is...

I'm looking for a text with loads of worked examples , plenty of exercises, and since I'm working alone , a solutions manual - or some access to the answers - is vital. Currently working Griffiths. The only way to master this demon is by doing dozens of problems. Any suggestions appreciated...

reading this http://uk.arxiv.org/abs/1004.2529 about supposed parallels between the mathematical structure of probability in QM and some problems in economics question is that are there really any violations of classical probability theory, such as Pr(A) > Pr(A \cup B) in QM? The supposed...

Hi there, I'm reading Dirac's Principles of QM, but I think I miss something... 1)When he derives the Poisson quantic bracket, he states that u_1v_1-v_1u_1=i\hbar[u_1,v_1] and says that hbar must be real since we introduced the imaginary unit. The thing is, since uv-vu is real, because we are...

Commutators on a discrete QM lattice = ? Please let me know if any of the following is unclear: I was thinking about how you could go about doing QM not in a continuous space but instead on a lattice, take 1D for simplicity. Let's use a finite (not countably infinite) number of positions say...

Homework Statement Show that: [p,x] = -iħ, Show that: [p,x^n] = -niħ x^(n-1), n>1 Show that: [p, A] = -iħ dA/dx Where p = -iħ d/dx, and A = A(x) is a differentiable function of x. Homework Equations [p,x] = px - xp; The Attempt at a Solution So far I understand part of each...

Sorry if this had been already discussed: http://arxiv.org/abs/1008.1066 So, what I see (assuming that Universe is infinite, this is an important assumption, not proven of course, but if this is true): 1. The 'Interpretation war' is over, amen, the most important weakness of MWI has...

I have been wondering if I should take Graduate level QM as an undergraduate. I'm currently signed up for a two quarter QM series, I have already taken a one quarter introduction to QM. I am a bit apprehensive as I am unsure if they assume vast QM knowledge (which I would sort of expect seeing...

Where I can read about Bohmian interpretation of QM? I need a good , solid book.

Dear All, This is my first post. I appreciate your help. I have the following question which i am struggling to understand, let alone solve. Consider a quantum mechanical particle with the mass m moving in one-dimensional described by the following Hamiltonian; (1)\hat{H} =...

I'm reading vol. 3 of the Feynman lectures on physics, and in chapter three he describes his third general principle of quantum mechanics as follows: "The third general principle: When a particle goes by some particular route the amplitude for that route can be written as the product of the...