Quantum mechanics Definition and 994 Threads

Homework Statement Here is a copy of the pdf problem set {https://drive.google.com/open?id=0BwiADXXgAYUHOTNrZm16NHlibUU} the problem in question is problem number 1 which asks you to prove the orthonormality of the spherical Harmonics Y_1,1 and Y_2,1. Homework Equations Y_1,1 =...

Homework Statement This is a (long) multi-part question working through the various stages of solving the radial Schrodinger equation and as such it would be impractical to type it all out here but I will upload the pdf (https://drive.google.com/open?id=0BwiADXXgAYUHOTNrZm16NHlibUU) of the...

Homework Statement Essentially we are describing the ODE for the radial function in quantum mechanics and in the derivation a substitution of u(r) = rR(r) is made, the problem then asks you to show that {(1/r^2)(d/dr(r^2(dR/dr))) = 1/r(d^(2)u/dr^2) Homework Equations The substitution: u(r) =...

Consider a cat in a box in a room. The box also contains some radioactive isotope. A geiger counter detects if the atom decays, and if it does, it sends a signal to some sort of computer, which causes a hammer to fall and smash open a bottle of poisonous gas. So, if the atom decays, the cat is...

Note this isn't actually a homework problem, I am working through my textbook making sure I understand the derivation of certain equations and have become stuck on one part of a derivation. 1. Homework Statement I am working through my text (Quantum Mechanics 2nd Edition by B.H Bransden & C.J...

Homework Statement I'm currently working on a homework set for my intermediate QM class and for some reason I keep drawing a blank as to what to do on the first problem. I'm given three potentials, V(x), the first is of the form {A+Bexp(-Cx^2)}, the others I'll leave out. I'm asked to draw the...

I flicker an LED on and off at a rate on the order of hundreds of kHz. The light, even though it is sent in pulses, still has its own frequency, correct? The frequency at which I turn the light on and off is not related to the frequency of the photons. Is this correct?

Homework Statement Show the mean position and momentum of a particle in a QHO in the state ψγ to be: <x> = sqrt(2ħ/mω) Re(γ) <p> = sqrt (2ħmω) Im(γ) Homework Equations ##\psi_{\gamma} (x) = Dexp((-\frac{mw(x-<x>)^2}{2\hbar})+\frac{i<p>(x-<x>)}{ħ})##The Attempt at a Solution I put ψγ into...

Homework Statement Obtain the matrix representation of the ladder operators ##J_{\pm}##. Homework Equations Remark that ##J_{\pm} | jm \rangle = N_{\pm}| jm \pm 1 \rangle## The Attempt at a Solution [/B] The textbook states ##|N_{\pm}|^2=\langle jm | J_{\pm}^\dagger J_{\pm} | jm \rangle##...

Homework Statement In classical physics, a system's magnetic moment can be written like so: \mu = g\frac{Q}{2M}L, where ##Q## is the total charge, ##M## is the total mass of the system and ##L## the angular momentum. a) Show, that for a cylinder (##I = \frac{1}{2}MR^2##) spinning around its...

Hi everyone, I wanted to know if any of you knows very good sources for quantum mechanics and spectroscopy fundamentals, like greats books, youtube videos (lectures), or any other option. I' m studying spectroscopy at the moment, and last year I've done the Physical Chemistry II course ( quantum...

Basically, I found the energy of a photon using its frequency ((6.8*10^15) and E=(3.6496394*10^-16)) and so I then used "p=E/c" to find the momentum and got 1.2173887*10^-24 however I don't know the measurement of the momentum. Is there a better equation to use to find momentum, and what would...

A diabatic process is defined as follows: Rapidly changing conditions prevent the system from adapting its configuration during the process, hence the spatial probability density remains unchanged. Typically there is no eigenstate of the final Hamiltonian with the same functional form as the...

Hello I'm an undergrad. Can anyone suggest me books, articles, lectures for studying quantum mechanics as a fresh starter? I tried r. Shankar but it only mathematical to me, couldn't get the physical significance. On the other hand, Griffith got way deep in concepts without sufficient examples...

Could somebody tell me good book about degenerate matter ?

Homework Statement I don't see how the author normalizes ##u(r)=Asin(kr)##. From Griffiths, Introduction to Quantum Mechanics, 2nd edition, page 141-142: http://imgur.com/a/bo8v6 Homework Equations ##\int_0^{\infty} \int_0^{\pi} \int_0^{2\pi}|A|^2 \sin^2(\frac{n\pi r}{a})r^2 \sin \theta...

In quantum mechanics, position ##\textbf{r}## and momentum ##\textbf{p}## are conjugate variables given their relationship via the Fourier transform. In transforming via the Legendre transform between Lagrangian and Hamiltonian mechanics, where ##f^*(\textbf{x}^*)=\sup[\langle \textbf{x}...

A. Neumaier submitted a new PF Insights post The Vacuum Fluctuation Myth Continue reading the Original PF Insights Post.

Homework Statement An electron is enclosed in a potential well, whose walls are ##V_0 = 8.0eV## high. If the energy of the ground state is ##E = 0.50eV##, approximate the width of the well. Answer: ##0.72nm## Homework Equations For an electron in a potential well, whose energy is less than...

Homework Statement In a potential box (##L = 1.00pm##) an electron moves at a relativistic speed, meaning it's momentum can't be expressed as ##P = \sqrt{2mE}##. a) Using the uncertainty principle, show that the speed is indeed relativistic b) Derive an expression for the allowed energy states...

Hey everyone, For my studies I have to read a part about approximation methods in Quantum Mechanics. Unfortunately I'm having difficulties understanding some concepts. If I'm correct, for describing a multi fermionic system of n electrons, the Hartree Fock (HF) method uses a Slater determinant...

Homework Statement A proton is known to lie within the nucleus of a gold atom. The radius of a gold nucleus is approximately 6 fm. What is the minimum uncertainty in the proton’s velocity [you may treat the problem as one-dimensional and you should express your answer as a fraction of c]...

Homework Statement Prove that ##[L_i,x_j]=i\hbar \epsilon_{ijk}x_k \quad (i, j, k = 1, 2, 3)## where ##L_1=L_x##, ##L_2=L_y## and ##L_3=L_z## and ##x_1=x##, ##x_2=y## and ##x_3=z##. Homework Equations There aren't any given except those in the problem, however I assume we use...

Hello. I'm studying quantum mechanics by my own. I'm targeting to be a condensed matter physicist. What is the best way to grasp the concepts as fast as possible,and what should I do to become a good physicist in the near future? Thanks. Note: I've got a bachelor degree in physics but I stopped...

From wikipedia I understand that the old quantum condition $$\oint_{H(p,q)=E} p_i dq_i = n_i h $$ states that not all kinds of motion are permitted in a system. My question is why is this called the old quantum condition and what is quantization of motion? Does this mean that a particle jumps...

Hello I am little bit confused about one topic on theoretical Physics and that is If we want to describe our Quantum world (example atoms in metal) then should I use Quantum field theory or Quantum mechanics?

Homework Statement Determine what colors of visible light would be absorbed by electrons in an infinite well, N = 3.1 nm. The effective mass for an electron in GaAs is one-fifteenth of the standard electron mass. Homework Equations En = πh2/[2*N2*me/15]*n2 L = nλ/2 Ψ = √(2/L)sin(nπx/L) The...

I've just watched a video by PBS spacetime on how an object with more potential energy has more mass, or less, in some cases (mass defect). But there is a problem. Quantum mechanics tells us that a particle has a chance of appearing at difderent places ( wave function), and that it also...

My question about the double slit experiment is this: why is it that nobody suspects that the detectors used to detect particles as they pass through the slits in the double slit experiment aren't causing some interference with the experiment which makes it seem as though they are acting like...

Sorry I keep posting about this. I had settled on Probability (Probability in discrete and continuous sample spaces; conditional probability; counting techniques; probability functions; binomial, Poisson, normal distributions; and transformations of variables.) based off of previous answers to...

Can quantum mechanics be derived from deeper principles? For example, special relativity results directly from the fact that the speed of light is the same for all reference frames. Conservation laws of momentum and energy come from certain symmetries of space and time. Does quantum mechanics...

I'm reading Gasiorowicz's Quantum Physics and at the beggining of chapter 2, SG introduces the concept of "wave packet" and gaussian functions associated to them. The first attached image is the 28th page of the book's 1st edition I suppose, and my question is about the paragraph inside the red...

Dear friends, Can "Modern Quantum Mechanics" by Sakurai be used as a first introduction to the quantum mechanics, given that I have a professor who can guide my reading and supplementary books? I recently got an opportunity for a reading course in rigorous QM, and I thought Sakurai would be a...

Hi! For the probability interpretation of wave functions to work, the latter have to be square integrable and therefore, they vanish at infinity. I'm reading Gasiorowicz's Quantum Physics and, as you can see in the attached image of the page, he works his way to find the momentum operator. My...

I apologize in advance for not being familiar with LaTex. 1. Homework Statement One thousand neutrons are in an infinite square well, with walls x=0 and x=L. The state of the particle at t=0 is : ψ(x,0)=Ax(x-L) How many particles are in the interval (0,L/2) at t=3? How many particles have...

Homework Statement Alrighty, so here's my problem in a nutshell: Some particle of mass m is confined to move along a ring of radius R. Since it's on a ring, it has periodic boundary conditions--i.e.: For the boundary defined as ##-\pi R \leq x \leq \pi R##, ## x = -\pi R ## and ## x = \pi R...

Hi, I am wondering about latent heat release when water freezes but it seems best to start with a regular exothermic reaction. How does bond formation create heat? What is actually happening at the microscopic level so that these combining particles are capable of causing adjacent molecules...

Do i need to go through classical mechanics, electricity and magnetism, thermodynamics and some other physics courses to start studying topics like quantum mechanics, astrophysics, gravitation and relativity?

Homework Statement Suppose we have a wavefunction with n=4. If we measure the orbital angular momentum along the z-direction(no spin in this problem) and get 2*hbar then what are the possible values of the total angular momentum and what is the most general wavefunction after the measurement...

I would like to know which chapters from the Advanced Quantum Mechanics textbook by Sakurai are most relevant to research work in high-energy theoretical physics. The kind of research topics that I have in mind pertain to work in string/brane cosmology, cosmological perturbations, dark matter...

I've heard good things about A Modern Approach to Quantum Mechanics by Townsend and Quantum Mechanics by Mcintyre. They use the same spin approach, but what are the pros and cons of each book?

How does the path integral formulation of quantum mechanics as given by ##\langle q_{f}|e^{-iHt/\hbar}|q_{i}\rangle = \int \mathcal{D}q(t)\ e^{iS[q]/\hbar}## make manifest aspects of quantum mechanics such as symmetries?

1. ##<x>= \int_{0}^{a}x\left | \psi \right |^{2}dx## ##\psi (x)=\sqrt{\frac{2}{a}}\sin\frac{n\pi x}{a}## then ##<x>= \frac{2}{a} \int_{0}^{a}x \sin\frac{n\pi x}{a}dx## 2. Homework Equations 1) ##y=\frac{n\pi x}{a}## then ##dy=\frac{n\pi}{a}dx## and 2) ##y=\frac{n\pi x}{a}## then...

Hello, I'm trying to understand how to calculate de probability of finding a system in a specific eigenstate using the density operator. In the book of Balian, Haar, Gregg I've found a good definition of it being the expectation value of the projector Pr in the orientation of the eingenstate...

Could someone tell me what the attached equation is called, and just and brief description of what it states. I don't recognise it and it's hard to know where one goes to just look up an equation. Thanks

The question here is simple; would the existence of virtual particles make the universe an open system? And if not, why? I thank all who consider this question for their time and would love to hear an answer.

Preface: As I understand it, according to quantum mechanics, there is a very good probability that I am sitting right in my chair right now, typing this question out. However, there is a non-zero, ever so small probability, however infinitesimally small chance that I am somewhere else in the...

I can't understand the solution to Problem 1.4(a). The solution is the following: What puzzles me is that ρ(θ)dθ=ρ(x)dx ? Why are they equal?

If we ever fully understood quantum science and all there is to know about it, could one say we then fully understand the universe? Or, would we never know at which point we know all there is to know? Would you be comfortable in the belief or proof nothing more could be discovered--about...

I was thinking that what is solid reason behind the failure of Classical Mechanics in Black body radiation? Why classical mechanics not explain the curve at lower or higher range of frequncies.