Wavefunction Definition and 572 Threads

I am given a non-normalized wavefunction and asked to normalize it. The function and the attempt will be in: http://i35.tinypic.com/2vahvuc.jpg

Homework Statement a particle of mass m, confined to a one dimensional infinite potential of 0\leqx\leq1 V(x) = 0 elsewhere V(x) = \infty Homework Equations Choose as a trial wavefunction \Psi(x) = Nx[1 - \alphax + (\alpha - 1)x^{2}] Verify that N^{2} = \frac{K}{16 -...

Homework Statement Normalise the wavefunction: \Psi(x) = C exp(-mwx^{2}/(2h)) for the 1-D harmonic oscillator. Homework Equations \int\Psi*\Psidx = 1 The Attempt at a Solution I used the following integral from -inf to inf: ¦C¦^2\intexp(-ax^2)dx = srqt(pi/a) where a = const...

Homework Statement consider a system with total angular momentum, l=1 in the state |\psi>=\frac{1}{\sqrt{2}}|1>-\frac{1}{2}|0>+\frac{1}{2}|-1> find |^{^}L_{\psi}> Homework Equations ^{^}L_{z}|\psi>=\hbar m|\psi>The Attempt at a Solution the basis in the wavefunction given are|1> , |0>, |-1>...

Homework Statement # The triplet state in helium atom is represented by a symmetric spin wavefunction. Are all triplet states of an atom represented by a symmetric spin wavefunction or is this just in the case of helium atom? # Fermions are represented by an anti-symmetric total...

Do you think the wavefunction is something which represents our knowledge of a system, or is it something physical? In the former case, could the same system be given a different wavefunction for different observers, depending on their knowledge of the system? From what I have learned of QM, it...

Hi everybody, it is usually said that the wavefunction of the localized particle at position x_0 is \psi_{x_0} = \delta (x-x_0). Is there some good reason for this? I mean, this function cannot be normalized, which means that |\psi_{x_0}|^2 cannot be interpreted as a probability...

The path taken by a ray of light, from an event E1 to event E2, follows a zero arc length curve such that E2 ∫ds = 0 1. E1 Where S is the interval along the null geodesic path between the...

I am trying to solve for the wavefunction for a particle inside a 2 dimensional disk of radius r_0. The conditions are: \int^{2\pi}_0 \int^{r_0}_0 |\psi|^2\, r \,dr\, d\theta = 1 Then I tried separations of variables (set psi = R(r)Theta(theta)) to solve the Schrodinger equattion. didnt'...

I’m hoping someone will help me fill in some holes in my understanding of the electronic wavefunction. I understand the electronic wavefunction to be a *complex valued* function of the positions of all electrons in the system. But, most descriptions of atomic orbitals refer to the various...

Hello all!:smile: I am at the QM-basics, and now a little bit confused, but maybe someone can easily clarify. A QM-system can be described by a state that lives in a hilbertspace, this was introduced because superposition is essential. In the solutions of different problems polynomial...

Hello: My question is simple: Does not the standard differential wave equation from Maxwell's relations lead to both positive and negative energy solutions for a photon's E field? If so, then why do we always throw away the negative energy solutions? Is this just custom? I suspect it is...

Homework Statement \psi(x)=\frac{3}{5}\chi_{1}(x)+\frac{4}{5}\chi_{3}(x) Both \chi_{1}(x) \chi_{3}(x) are normalized energy eigenfunctions of the ground and second excited states respectivley. I need to find the 'wavefunction in the energy representation' The Attempt at a Solution...

Homework Statement 1) The probability density at certain points for a particle in a box is zero. Does this imply that the particle cannot move across these points? There was also 2 figures that go with it, but I don't know if it's possible to upload them. One shows psi against the length of...

In NMR for molecules, one can collapse the nuclear spin wavefunction \psi_{nucspin} by applying the magnetic moment operator \mu. That is, \psi_{nucspin} becomes one of the eigenfunctions of \mu. This physically corresponds to hitting the nuclei with photons in the radiofrequency range. In...

If we solve the Schrodinger Equation for hydrogen atom, we get discrete energy levels that agree with experiment. But no where we need the wave function collapse. So my question is where the wave function come from and why do we need it?

Hi, I have always read the texts in which they have mentioned that for the electrons which are fermions the wave function should be antisymmetric, but I have not yet found a good proof for that. In some books they have mentioned the pauli's exclusion principle and some relations, but still...

Hi folks, I'm not sure if it's best to ask this question here, or in the Special & General Relativity section - it's probably more appropriate for this forum. I've been wondering about the following question: what effect does wavefunction collapse have on space-time? For example, if we...

I just started learning QM. I was wondering, if a wavefunction can only collapse onto a few eigenstates, how come the probability distribution graph is a usually continuous one? :S

Homework Statement Nothing that big, just some questinos that i had about wavefunctions. i was reading this handout and came across this. Suppose i am given an equation of a wave function, how do i know whether or not does it describe the state of definite energy and/or in the state od...

i am a amature at quantum mechcanics unfortuatly. i need to understand wavefunction but i cannot find a site that explains it fully does anyone have any suggestions?

I was told that if there is a wavefunction containing a proton and a neutron that it must be anti-symmetric under exchange of a proton and a neutron. I am having trouble understanding this. The short handwavy explanation is that they are indistinguishable via the color force. What bothers...

Does anyone know a deeper reason why the quantum mechanical wavefunction has to be complex? Is it to incorperate time dependence? Or maybe the operator/eigenvector formulation is special and since it includes the scalar product, having complex variables is more general and necessary? Or...

Dear All: Any idea for the following interesting question: As we know we can calculate inner product of two wave functions A and B as <A|B>. here both A and B are vector in hilbert space. here we may use fourier transform to get momentum representation of A and B, and get same...

I am solving the Hydrogen wavefunction using FORTRAN. Now using the Euler method, I am given a solution to match which is given by u10(r) = 1.06r*exp(-3.74r) (where unl(r) = rRnl(r) in general) which says it has a normalisation chosen to match what i should get from my code. Then I use the...

I am solving the Hydrogen wavefunction using FORTRAN. Now using the Euler method, I am given a solution to match which is given by u10(r) = 1.06r*exp(-3.74r) (where unl(r) = rRnl(r) in general) which says it has a normalisation chosen to match what i should get from my code. Then I use the...

Homework Statement This is the first question from a past exam paper I'm doing at the moment, and I'm not sure if it's a case that I'm doing something stupid, or if there is a problem with the question. Q: The wavefunction of a deuteron can be approximated by: \psi (r) = \frac{C}{r}...

In QM, sometimes we will combine the delta potential and other familiar potential (like infinite potential well). And I am quite confuse with the bound state. For example, consider a 1D infinite potential well with width a and locate b/w [-a/2, a/2]. Now if we add in a delta potential...

Hi, I have been given a differential equation to use in order to solve for the Hydrogen wavefunction in the ground state using Euler's method. d^2u_nl/dr^2 -(l(l+1)/r^2)*u_nl + 2k*(E_nl-V(r))*u_nl = 0 V(r) = -a/r where a = 1/137.04 I have been given initial conditions u_nl(0) = 0 an...

Dear all, I have a question about the sign of Schrodinger equation in particle in a box. What's the meaning of the sign (like -, +) of wavefunction in particle in a box? Can anybody explain that? Thank you.

Homework Statement This isI n't formatted properly because I don't have much time. The wave function is f(x) = e^-|2x| I need to normalize this functionHomework Equations The normalization condition is S f^2dx=1 (that S is an "integral" sign and the limits are from - infinity to +...

Dear, I have a trouble understanding QM. What's the difference between wavepacket and wavefunction? Can we use a wavepacket for a particle in a box? Please reply to this questions. Thank you in advance.

Hi everybody, I'm studying Hartree-Fock theory. It is written that, in Hartree approach, for the two electrons in positions r1 and r2 (these are vectors, of course), the joint wavefunction of this 2-particle system is given as Psi(r1, r2)=Psi1(r1) * Psi2(r2) I'm confused a lot at this...

Homework Statement Find the wave function of particle in a 1-dimensional potential Well of length L, n=2 and mass m Homework Equations I think this would be the wave equation, but not 100% sure [tex]\varphi=Asin(n\pix/L)[\tex] where n=1,2,3... tex doesn't work for me---=Asin[n*pi/L] The...

Hi all, a couple of weeks ago, I was reading a book (Eisberg and Resnick) in which one of the questions asked was: Basically, the book doesn't give the answer and I don't know it. I also can't work it out, despite the past two weeks of wracking my brain over this problem. Can anyone offer a...

Homework Statement A Quantum mechanical particle is defined by the following wave functions: \Psi(x) = Aeax for x<0 \Psi(x) = Ae-2ax for X>0 where A and a are both real, positive constants. Normalize the wavefunction, i.e. determine an expression for A in terms of a. Homework...

hello, friends in this forum. Do you provide me some cues in calculating the many-body wavefunction? such as the fpu-beta model, the Hamiltonian of it is H=\sum_{i=1}^{N}\frac{p_{i}^{2}}{2}+\frac{(x_{i}-x_{i-1})^{2}}{2}+\frac{(x_{i}-x_{i-1})^{4}}{4} ,Thank you!

Homework Statement A wavefunction for a hydrogen electron is given by \Psi = - \sqrt{\frac{3}{8 \pi}} sin\theta e^{i \phi} (\frac{1}{2a^3})^{3/2} \frac{re^{-r/2a}}{a \sqrt{3}} Prove that the electron exists in space, ie, \int {\Psi}^2= 1 2. Homework Equations & attempt at...

1. At a certain time the wavefunction of a one-dimensional harmonic oscillator is \psi(x) = 3\phi0(x) + 4\phi1(x) where \phi0(x) and \phi1(x) are normalized energy eigenfunctions of the ground and first excited states respectively. Normalize the wavefunction and determine the probability...

Uncollapse of a partial-collapsed quantum state has been accomplished in the laboratory. Here is a popular article http://www.scienceagogo.com/news/20080706233709data_trunc_sys.shtml An article on this by Nadav Katz et al has just appeared in Nature News. I believe this is the preprint of...

Why shud one take the Fourier transform of a wavefunction and multiply the result with its conjugate to get the probability? Why can't it be Fourier transform of the probability directly? thank you

Hi everyone, This might belong in the quantum mechanics section, so I apologize if I placed this thread in the wrong place. My question is: how do I calculate the gradient of a multiparticle wavefunction? For example, suppose that a wavefunction \psi describing the probability...

Problem A free particle of mass m moving in one dimension is known to be in the initial state \psi(x, 0) = \sin(k_0 x) a) What is \psi(x, t)? b) What value of p will measurement yield at the time t, and with what probabilities will these values occur? c) Suppose that p is measured at...

Problem Describe the evolution in time of \phi_1 = A \sin \omega t \cos k(x+ct). Attempt at Solution We have that \partial^2 \phi_1 / \partial x^2 = -Ak^2 \sin \omega t \cos k(x+ct) \partial \phi_1 / \partial t = A \sin \omega t (-kc \cdot \sin k(x+ct)) + A \omega \cos \omega t \cos...

Wavefunction collapse ==> increase in entropy?? I just read an article in Scientific American by Sean Carroll, called something like Does Time Run Backward in Other Universes. In it, he says that the reason wavefunctions only collapse and never un-collapse is because collapsing represents an...

If in the case of two non-interacting particles, the wavefunction looks like (for bosons): \psi(x_1, x_2) = \frac{1}{\sqrt{2}}[\phi_a(x_1)\phi_b(x_2) + \phi_a(x_2)\phi_b(x_1) And to normalise the wavefunction, the modulus squared has to be found. I can do this when I can substitute...

I'm not sure the double-slit experiment is one such example, maybe I have not understood it yet. This experiment shows the wave nature of light due to the wavefunctions of photons. But how does it show a particle of zero size that is not just a burst of waves?

Hi, I'm teaching myself quantum mechanics (so this isn't homework). I came across the following question: \Phi(p) = A\Theta\left[\frac{\hbar}{d}-|p-p_{0}|\right] I have to find the constant of normalization, \psi(x), and the coordinate space wave function \psi(x,t) in the limit...

[SOLVED] Perturbed Ground State Wavefunction with Parity Homework Statement A particle is in a Coulomb potential H_{0}=\frac{|p|^{2}}{2m} - \frac{e^{2}}{|r|} When a perturbation V (which does not involve spin) is added, the ground state of H_{0} + V may be written |\Psi_{0}\rangle =...

Could anyone please help with the following, rather unusual, query? I know that for spin 0 bosons, the Klein Gordon equation gives solutions that are similar to the solutions of the Schrodinger equation for a non-relativistic free particle, the only difference being that the energy used when...