Wavefunctions Definition and 139 Threads

Homework Statement 1. I got the wavefunctions:\psi _0=(\frac{m\omega }{\pi\hbar})^{\frac{1}{4}}\cdot e^{-\frac{m\omega}{2\hbar}\cdot x^2}, and \psi _1=(\frac{m\omega }{\pi\hbar})^{\frac{1}{4}}\cdot \sqrt{\frac{2m\omega }{\hbar}}\cdot e^{-\frac{m\omega}{2\hbar}\cdot x^2}. Also recomended by...

I am having trouble understanding how a wavefunction for three or more particles can be totally antisymmetric. Does this just mean that the sign stays the same for even permutations of the indices, while the sign changes for odd permutations (i.e., is it just antisymmetric like a rank three tensor)?

Hello, we started Quantum Mechanics last semester, and somehow I manged to do most of the homework during that semester, but now I'm trying to revise it again, and I can't seem to understand the very basics of it, in particular about wavefunctions. Please read this carefully, because you might...

I'm having a little trouble recreating some things from a paper and it is due to my lack of knowledge of working with Flavor-Spin wavefunctions. I'm trying to show that : \left\langle \Lambda \left|b_s^{\dagger }b_b\right|\Lambda _b\right\rangle =\frac{1}{\sqrt{3}} and \left\langle p...

Hello all, This may be my very first post on Physics Forums. I am a 1st year physics grad student and need some help on something that's been bugging me. Suppose we have two spin half particles in a bound state. The total spin will either be 0 or 1. The spin 0 state, for example, would be...

Homework Statement Hi all. I wish to evaluate the following dipole moment <1| x |2>, where |1> and |2> are stationary states of the hydrogen atom when one accounts for spin-orbit coupling. I am a little unsure of if I am allowed to use the "normal" unperturbed wavefunctions for...

A particle is described by the normalised wavefunction; $ \psi (x,y,z) = Ae^{- \alpha ( x^{2} + y^{2} + z^{2} ) }$ Find the probability that a particle is in a dr shell of space. For what value of r is the probability of finding this particle greatest, and is this the same r value...

Homework Statement In spherical polars, the azimuthal part of the wavefunction of a particle is psi(phi) = 1/sqrt[2.pi] . exp[i.m.phi] where phi is the azimuthal angle. Show m must be an integer.Homework Equations I know you are supposed to have a good go at solving the problem first, but...

if you have a wavefunction for an electron in one orbital and another wavefunction for the same electron in another orbital and assuming that the electron transitions from the one to the other orbital how would you derive the frequency of the emitted light from the wavefunctions themselves...

I know what orthogonal means (well, I know orthogonal vectors are perpendicular to each other) but how can this be applied to a wavefunction? Thanks!

What is the basis to say that the wavefunction of a multi-electron system is the product of individual wavefunctions of the electrons that form the system? In other words, how does theory ensure that the multi-electron wavefunction is seperable into variables r1 and r2? Even in Hartree...

Sorry for not using template but you should find everything in the image provided: Hey guys. All of the info for the problem is in a picture. I've tried working on this for ours and I still can't seem to get the trig identities right :(...

Homework Statement Hi all. If I have two normalized wavefunctions f and g, will their product fg also be a normalized wavefunction? Thanks in advance. Niles.

Homework Statement Hi all. I am looking at a potential with two wells, where we denote the wells a and b. Now there are two electrons in this setup, which we label 1 and 2. I have the following innerproduct: \left\langle {\phi _b (x_1 )} \right|\left\langle {\phi _a (x_2 )}...

Homework Statement Hi all. My question is best illustrated with an example. Please, take a look: Let's say we have particle in a stationary state, so \Psi(x,0)=1\cdot \psi_{1,0}(x) with energy E_{1,0}. Now at time t=0 the Hamiltonian of this particle changes, since the particle gains some...

Prove that the probability of finding a particle of mass m in a one-dimensional potential well of length L is 0.5 for both the first and second half of the well for the state with n = 2. Demonstrate that these results make sense in light of the form of the wavefunction for each case. Someone...

Wavefunctions spread with time, if the particle does not interact. Now, the universe is filled with particles that do not interact for thousands and millions of years, for example cosmic ray protons. This would mean most space in the universe is filled with wavefunctions, all...

This might be a silly question, but do protons and neutrons have a wave function that they can be described by?

I just want to make sure I understand this point: The eigenfunctions of the hydrogenic Hamiltonian are \varphi_{nlm}=R_{nl}Y^{m}_{l} If I need to find the probability of finding the electron in the nucleus (in r<R0), and I use the normalized R_{nl}, can I simply calculate the integral...

I found out the Coefficient expansion theorem and constructed the following wavefunction: Ψ(x,0) = 1/sqrt(2)*Φ1 + sqrt(2/5)*Φ3 + 1/sqrt(10)*Φ5 where φn = sqrt(2/a)*sin(n*pi*x/a) Is this unique why or why not? I'm thinking that it has something to do with all odd Energies. Also is...

[SOLVED] molecular orbital wavefunctions http://img255.imageshack.us/img255/7012/37626561fb6.jpg starting with Sz(total) = Sz1 + Sz2 Sz(alpha) = +(1/2)hbar(alpha) Sz(beta) = -(1/2)hbar(beta) I first found the determinant and then simplified psi =...

This is the way I understand it. Correct me if I'm wrong. A 'particle' in a given situation will be in a state |\psi>, which is determined by the Schrodinger Equation. After measurement, the particle will then go to a state |\omega>, where |\omega> is an eigenvector of the operator...

Homework Statement I am working on 6.16 at the following site: http://mikef.org/files/phys_4241_hw14.pdf I think that the solution given is given is wrong. I can get part a), however, I am just getting stuck on part b). So, the wavefunction in r < r_0 is R(r) = A/r sin(k_1*r) and the...

Ok I have two orthonormal wavefunctions of a system, \psi 1 and \psi 2 and \widehat{A} is an observable such that \widehat{A} |\phi _{n} > = a_{n} |\phi _{n} > for eigenvalues a sub n what are the probabilities p1(a1) and p2(a2) of obtaining the value a sub n in the state |psi1> and...

what is the use of representing wavefunctions say \psi(x,t)=A\cos(kx-\omega t) by \psi(x,t)=Ae^{i(kx-\omega t)} when we actually mean the real part

are spinors just wavefunctions in the dirac field?

Page 152 Robinett: Consider the (non-normalized) even momentum space wavefunctions for the symmetric well:, \phi_n^+(p) = 2sin(w-m)/(w-m)+sin(w+m)/(w+m) where w = sin((n-1/2)pi) and m = ap/hbar. Show that \int_{-\infty}^{\infty}\phi_n^+(p)^*\cdot \phi_n^+(p) dp = \delta_{n,m} The hint...

Hi, I have a question about the discussion of the free-electron (Fermi) gas in my solid-state physics notes. In the free electron model, you basically have particles in a box, and the state of any particle is described by four quantum numbers, nx, ny, nz, and ms, the spin magnetic quantum...

Homework Statement Consider two noninteracting particles p and q each with mass m in a cubical box od size a. Assume the energy of the particles is E = \frac{3 \hbar^2 \pi^2}{2ma^2} + \frac{6\hbar^2 pi^2}{2ma^2} Using the eigenfunctions \psi_{n_{x},n_{y},n_{z}} (x_{p},y_{p},z_{p}) and...

bb] The dipole transition amplitude for the transition (nlm) -> (n'l'm') is given by [/b] \int \psi_{n'l'm'}^* \vec{r} \psi_{nlm} d\tau Is the dipole transition amplitude simply a measure of how likely a certain transiton is?? Heres another question In converting \psi_{nlm_{l}m_{s}} =...

I'm reading Harrison's book on Solid State Theory, and he states without explanation that the many-particle wavefunction in a solid must be anti-symmetric with respect to exchange of any two electrons. I guess it may be obvious, but can someone explain why it's anti-symmetric?

Born's conditions for an acceptable "well-behaved" wavefunction F(x): 1. it must be finite everywhere, i.e. converge to 0 as x -> infinity 2. it must be single-valued 3. it must be a continuous function 4. and dF/dx must be continuous. I'm having difficulty understanding the last...

Hi - hope that someone can help me with this. I am new to quantum mechanics - trying to answer a question about eigenfunctions and don't have a decent textbook at the moment. Can someone tell me please, what is the difference between a wavefunction and an eigenfunction for a particle in an...

On a recent thread about cloud chambers, a question popped into my head. My knowledge of cloud chambers is that one can see the "path" of certain elementary particles as they pass through the chamber. If, say, we had an electron passing through the chamber, do we have to assume that the...

Every one knows that wavefunctions are generally complex functions described by three quantum numbers n, l and m, and the number m is included in the form exp(i*m*fai). But here in the following webpage they are all real functions, I'm confused:confused: . Can anyone help me? Thank u in advance!

Hi, State vectors ("kets") live in Hilbert space. Do wavefunctions also live in Hilbert space? I've read that they both do, but how can functions and vectors reside in the same space? Or do wave functions simply map from coordinate space to Hilbert space...

I am not sure if my title to this thread is appropriate for the question I am about to ask, but it is what we are currently studying in my Quantum Mechanics class so here it goes. Two non-interacting particles with mass m, are in 1-d potential which is zero along a length 2a and infinite...

Hi! Two (distinguishable) non-interacting electrons are in an infinite square well with hard walls at x=0 and x=a, so that the one particle states are \phi_n(x)=\sqrt{\frac{2}{a}} sin(\frac{n\pi}{a}x), E_n=n^2K where K=\pi^2\hbar^2/(2ma^2) My question is what are the spins and space-spin...

Well, a week ago my Professor said the space of quantum physical states was a Hilbert space. Thing is, he just said it, and moved on. So I have a vector space with a scalar product. Is it, indeed, Hilbert? That is, is it complete? I guess I'll see the answer next semester, in real functions...