Quantum mechanics Definition and 994 Threads

I'm planning to get a copy of Quantum Mechanics - Modern Development by L. E. Ballentine. However I am uncertain between the first and second editions. The first edition is cheaper. I will be using it for my PhD research with the topic of atomic physics. Will the second edition give me...

Homework Statement We are given the Hamiltonian H and an observable A ##H=\begin{pmatrix} 2 & 0 & 0\\0 & 0 & 1\\0 & 1 & 0 \end{pmatrix}\hbar\omega A= \begin{pmatrix} 1 & 0 & 0\\0 & 1 & 0\\0 & 0 & -1 \end{pmatrix}a ## We are also told that at ##t=0## we have that a measurement of A gives us...

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 ...

If a photon A is entangled with photon B and one somehow destroys photon A, what will happen to photon B? Will it also get destroyed? And can two entangled photons combine into one?

Hi everyone, I'm new to Physics Forums and to Mathematica, as well as Jacobi Identity. In any case, I was wondering on how I may use Mathematica to solve various Quantum Mechanics related problems through commutators. Like if it's possible to find out what is the form of a particular commutator...

Homework Statement Consider A(x) is an arbitrary function of x, and px is the momentum operator. Show that they satisfy the following condition: [px,A(x)] = (-i/ħ)*d/dx(A(x)) where [px,A(x)] = pxA(x) - A(x)px Homework Equations ħ = h/2π px = (-iħ)d/dx The Attempt at a Solution Starting with...

Hi everybody I'm currently looking for an introductory quantum mechanics book which emphasizes the mathematical aspects of it. I especially need exercises in order to pass a written exam, but I'd like to have even lots of examples. I've already gone through the whole "Picasso" (it's an italian...

Homework Statement In Zettili's QM textbook, we are asked to find the trace of an operator |\psi><\chi| . Where the kets |\psi> and |\chi> are equal to some (irrelevant, for the purposes of this question) linear combinations of two orthonormal basis kets. Homework Equations...

Homework Statement A conduction electron moves through a block of Cu until it reaches the surface. At the surface the electron feels a strong force exerted by the nonuniform charge distribution in that region. This force tends to attract the electron back into the metal which is what causes the...

I understand why a black body absorbs every frequency(it is the definition of a black body!) but i do not understand why it also radiates at all frequency spectrum.

Wikipedia writes: "Black-body radiation is the type of electromagnetic radiation within or surrounding a body in thermodynamic equilibrium with its environment". Why does it write "thermodynamic equilibrium"? If it is not in a thermodynamic equilibrium, then what changes as far as the absorption...

Suggest for a reference book for quantum mechanics having detailed theoretical explanation and lot of solved examples.

0http://stackoverflow.com/questions/34833391/tannor-quantum-mechanics-derivative-of-variance-of-position# In the Tannor textbook Introduction to Quantum Mechanics, there is a second derivative of chi on p37. It looks like this: χ"(t) = d/dt ( (1/m) * (<qp + pq> - 2<p><q> ) (Equation...

I was thinking about a laser, a very strong laser, how does it "burn" things? And what about the microwave oven? What happens in the atomic scale? I know that when something has an increase in temperature the atoms moves quicky because the the temperature is proportional to the kinetic energy...

So I have not been able to find too much information about this. Specifically in the context of the double slit experiment. I've seen just about the only video on Youtube that tries to explain this, but I did not understand-- I felt like somethings were not explained. I am acquainted with why a...

I will be taking a first course on Quantum Mechanics and just wanted to know what kind of ordinary differential equations must i know before going into the course. Thank you!

Look at the following derivation: ## p=\frac{im}{\hbar}[H,r] ## if ##H|\psi\rangle=E|\psi\rangle##, then ## \langle \psi|p|\psi \rangle = \frac{im}{\hbar}\langle \psi|Hr-rH|\psi \rangle = \frac{im}{\hbar}\langle \psi|r|\psi \rangle(E-E)=0 ## What's wrong with my derivation or it is true that...

What parts of Classical Mechanics must someone know before studying Quantum Mechanics in order to understand the former in all its glory? Thank you

Without getting too deep into the physics or philosophy of quantum mechanics, and I'm NOT talking about theory (no 'what the equations say') but if I'm not looking at my couch does that it mean at the moment it doesn't exist? Or if I'm not looking at my dad he isn't there but in the form of a wave?

Let's be fair, it's not true. Pure states are the ones that correspond to exact physical states. And it is not intuitive that exact physical states should transform continuously. Our belief about outcome can transform continuously but belief does not correspond to pure state.

Hello. I am not too sure if this thread is the right place to post this in. But anyway. I have to make a project for my final year, and I have chosen to make a quantum mechanics based project. I am thinking of doing some quantum mechanics based simulations, give a little bit of history of...

Does quantum mechanics have to be weird? It sells much better to the general public if it is presented that way, and there is a long history of proceeding that way. But in fact it is an obstacle for everyone who wants to truly understand quantum mechanics, and to physics students who have to...

What I'm going to need to learn from this book? I'm going to need read something before?

Homework Statement For an infinite potential well of length [0 ; L], I am asked to write the following function ##\Psi## (at t=0) as a superposition of eigenstates (##\psi_n##): $$\Psi (x, t=0)=Ax(L-x) $$ for ## 0<x<L##, and ##0## everywhere else. The attempt at a solution I have first...

Consider a system with countable quantum states. One can define Jij as the rate of transition of probability from i-th to j-th quantum state. In H-theorem, if one assumes both $$ H:=\Sigma_{i} p_{i}log(p_{i})$$ $$J_{ij}=J_{ji}$$ then they can prove the H always decrease. The latter is Fermi's...

Hello!can someone propose a good textbook for quantum mechanics and mathematical physics(including green function)?I would like to buy those books so i want something which is one of the best to have in your libraby!

For an electron can I not do the following to determine both the position and momentum? I take a screen with a small hole and I eventually make the hole smaller and smaller. Cathode rays emitted will hence get diffracted after passing through the hole making momentum more and more uncertain...

I took quantum mechanics 1 this semester. It's part one of two that I need to graduate. I received a D in the course. I'm not sure if the D prohibits me from taking quantum 2 next semester. I'm still waiting to hear back from my advisor. The course catalog doesn't say that a C or better is...

Homework Statement Define n=(x + iy)/(2)½L and ñ=(x - iy)/(2)½L. Also, ∂n = L(∂x - i ∂y)/(2)½ and ∂ñ = L(∂x + i ∂y)/(2)½. with ∂n=∂/∂n, ∂x=∂/∂x, ∂y=∂/∂y, and L being the magnetic length. Show that a=(1/2)ñ+∂n and a†=(1/2)n -∂ñ a and a† are the lowering and raising operators of quantum...

Homework Statement A linear harmonic oscillator with frequency ω = hbar / M is at time t = 0 in the state described by the wave-function: Ψ(x,0) = C( 1 + √2x) e-x2/2 Determine the values of energy which can be measured in this state. I'm not really sure where to start this question and was...

Why is Quantum mechanics probabilistic? what prevents it from being deterministic, like classical mechanics ?(is it the lack of information about the processes and the forces applied at this scale?)

I studied this from Griffith Chapter 2, with the algebraic (raising and lowering operator) method, we reached the ground state by setting a_Ψ0 = 0 , then we got what the ground state is, and then plugged it in the Schrodinger equation to know the energy, and it turned out to be 0.5 ħω. My...

I'm teaching advanced undergraduate quantum mechanics in the spring for the first time, using Griffiths' Introduction to Quantum Mechanics. (It's basically "mathematical methods of quantum mechanics: eigenstates, bra-ket notation, ladder operators, WKB approximation, etc). If you've taken or...

Homework Statement The question is here. http://postimg.org/image/l7aw07sr9/ Homework EquationsThe Attempt at a Solution I don't even understand what it's asking because how can a stationary state be an exponential function with no boundaries? I would appreciate any insight, thank you.

this question is a bit philosophical... in general relativity time "doesn't exist", and all of spacetime is already a preexisting pseudo riemannian manifold. however experiments have only shown time run at different rates, not that spacetime is preexisting. in our ordinary experience time is...

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...

Hello, I really need a good book on ordinary differential equations with applications on Quantum Mechanics, as I will be attending a course on QM but I do not have the proper mathematical background that is needed.

Homework Statement Verify that a plane wave ψ(x) = Ae-ikx is a solution to the time independent Schrodinger equation for a free particle in one dimension. Can it be normalised? Why?[/B]Homework EquationsThe Attempt at a Solution My lecturer's notes are all over the place, which is frustrating...

Homework Statement Suppose that two neutrinos are created in the sun - call the states |{ \nu_1}\rangle and |{ \nu_2}\rangle . (Among many other things) I am asked to show that once the neutrinos have propigated a distance x after a time t, the states satisfy: |{ \nu_1}(x,t)\rangle =...

Whole my life I have been interested in Quantum Physics. I have a bachelor degree in IT. I did not finish my studies. I have always been quite sloppy in studying in school. As a result, my mathematics skills are terrible. I often get pointed out on this forum that I better start with the...

Hello, I've been reading the Stern-Gerlach experiment, and where the concept of electron spin is introduced, am facing a problem, i.e., if you consider electron a charged rotating sphere, then the electromagnetic energy and size of the electron becomes huge! So how do you deal with this? Thanks...

Homework Statement Homework Equations This is a passage from Modern Quantum Mechanics by Sakurai ( page 26~27) The Attempt at a Solution I wonder how i can get 1.4.8 , 1.4.9 equations . and what do they mean?

Hello again, Am facing a difficulty, the question is that , Is energy and momentum conserved for a particle in an infinite square well, at the boundary i.e, at x=a, where the potential suffers an infinite discontinuity?? V=0 for -a<=x<=a V=infinite else-where Thanks in...

Dear Physics Forum personnel, I am a college student with double majors in the mathematics and computer science. I recently got interested to the art of quantum mechanics course through my current undergraduate research in the theoretical computer science, where my near-future project will...

Homework Statement Find the energy levels of a spin ##s=\frac{3}{2}## particle whose Hamiltonian is given by: ##\hat{H}=\frac{a_1}{\hbar^2}(\hat{S}^2-\hat{S}_x^2-\hat{S}_y^2)-\frac{a_2}{\hbar}\hat{S}_z## where ##a_1## and ##a_2## are constants. Homework Equations In the ##\hat{S}_z## basis...

What are some reputable, trustable websites that explain quantum mechanics and all its concepts well? Also, what are some good books about quantum mechanics? (Note: This is for the general ideas of quantum mechanics as a whole.)

Hi, I am currently watching this lecture series, and was wondering about something. At some point the lecturer says that QM is "not quantized", because if you express your solution to the schrodinger equationby introducing a pertubation parameter \epsilon, you will go smoothly from one...

Homework Statement Show that δ(x-x') = d/dx Θ(x-x') Homework Equations ∫ f(x') δ(x-x') dx' = f(x) Θ(x-x') vanishes if x-x' is negative and 1 if x-x' is positive The Attempt at a Solution I saw a relation of the δ function but I don't know why is it like that. Integral of δ(x-x') from -∞ to x...

Hello, before I start off, I apologize for asking a question which I am sure has been asked hundreds of times before: but I felt there is just way too much information out there which is a little confusing, so I am here with the hope of getting some personalized suggestions. I am currently a...