Wavefunction Definition and 585 Threads

Regarding Rayleigh and Raman scattering: I'm trying to understand the implications of the Raman wavefunction, being time independent. It certainly makes the derivation of the resonance Raman cross-section simple, but I'm struggling to understand the role of the imaginary component...

[problem is: the wavefunction for a particle in a stationary state of a one dimensional infinite potential well is given by: \Psi_{1}(x,t)=A\cos(\frac{\pi x}{2a})e^{-i\frac{Et}{\hbar}} for -a\leq x\leq a = 0 otherwise. using the normalised wavefunction calculate the expectation value...

Node and Nodless wavefunction? What means Node and nodeless wave functions? Nawzad A.

Homework Statement Show that the rotational wavefunction 3cos2? -1 is an eigenfunction of the Hamiltonian for a three dimensional rigid rotor. Determine the corresponding eigenvalue. Homework Equations the eigenstates are |l,m> the quantum number of the total angular momentum is l...

For a system of N bosons that are non interacting, the wavefunction is given by: SQRT[1/N!.n_1!.n_2!.n_3!...] SUM P. A_1.A_2.A_3...A_N Where the sum runs to N! and the P is the permutation operator, swapping 2 particles at a time. n_i is the number of particles in the nth energy state...

Homework Statement What fraction (as a percentage) does the n=(2x2-1)th infinite potential well wavefunction contribute to the 'classical' initial wavefunction psi(x,t=0)=1/sqrt(L) ? (Why are the even n excluded?) Homework Equations psi(x,t=0) = 1 / sqrt(L) The Attempt at a Solution...

Do wavefunctions have to have every conceivable possibility? Say for instance you have a chair. Does the wavefunction of the chair necessarily have a possibility where the chair breaks apart spontaneously? Or a set of worlds where the chair breaks apart if MWI is true? Or can the wavefunction...

Homework Statement Can this function be a wavefunction of a physical system with finite potention energy: \psi(x)=\frac{A}{\sqrt{x^2+b^2}}Homework Equations noThe Attempt at a Solution The ans is YES. 1)it is continuous. 2)its derivative also continous. 3)It can be normalized, as it tends to...

Homework Statement Ok so I am told that the angular part of a system's wavefunction is: Psi (theta, phi) = root2 cos(theta) -2i sin(theta) sin (phi) Now I am trying to normalise it.. Homework Equations The Attempt at a Solution Psi * (theta, phi) = root2 cos(theta) + 2i...

Homework Statement A particle in the infinite square well with V(x)=0 for 0<x<a and V(x)=infinity otherwise has the initial (t=0) wave function: psi(x,0)=Ax for 0<x<a/2 psi(x,0)= A(a-x) for a/2<x<a 1) Sketch psi and psi^2 (DONE) 2) Determine A [DONE - 2*sqrt(3)*a^(-3/2)] 3) Find psi(x,t)...

On my notes, the lecturer left out some of the formulae as blanks which we were supposed to fill in as we went a long but I'm missing a few of them. The 1st one is: [PLAIN]http://img213.imageshack.us/img213/6627/screenshotdh.png I'm stuck here, I can't figure out what equation he's...

If matter goes from a superposed state to a collapsed state when measured, how did scientists see the interference pattern in the double slit experiment, doesn't the surface that the photons hit after passing through the slits count as a measuring device? Also, is there any updated...

Hi.. In a textbook, the ground-state wavefunction for any general Hamiltonian was under consideration. Then, a statement was made that this wave function is real since it is the ground state. Is it true that one can always choose the ground state wave function to be real? I understand...

If I fire a stream of electrons at a CRT screen, the electrons go pretty much where I point them (this is how CRT Tv's work). But from reading popular science books I am led to believe that until the electron hits the screen, it has a range of possible positions and can in theory appear in any...

Is the wavefunction of a particle really shaped like a wave? A lot of analogies are made about how the wave function is like a water wave which can interfere with other waves. But does the schrodinger equation truly produce something shaped like a wave (ie a 3d sine wave) when plotted?

1) Macroscopic objects have their own wavefunction, right? Would this wavefunction include physical attributes that would contain possibilities for certain features that macroscopic objects have (say the macroscopic object is a bed – the wavefunction would have possibilities for all the...

Homework Statement You are given in a earlier stage of this problem that the wavefunction is separable, ie.) \Psi(x,y) = X(x)Y(y) The problem asks you to solve for the wavefunction of a particle trapped in a 2D infinite square well using Parity. ie.) solve \Psi(-x,-y) = \Psi(x,y) and...

How you obtain the Wavefunction of a system? \Psi = A e^{kx + wt} I get it that you can plug this in the Schrodinger equation, but what I don't get is how you obtain the parameters experimentally ?

The wave function for a particular electron is given by: Psi= 4/(9√(4π)) * (6/a)^(3/2) * (r/a)^2 * e^(2i(phi) - (2r)/a) * sin^2 (θ) a) This is an electron in which subshell? b) This is an electron in an atom of which element? c) What is the ionozation energy for this electron, assuming...

The wave function for a particular electron is given by: Psi= 4/(9√(4π)) * (6/a)^(3/2) * (r/a)^2 * e^(2i(phi) - (2r)/a) * sin^2 (θ) a) This is an electron in which subshell? b) This is an electron in an atom of which element? c) What is the ionozation energy for this electron, assuming...

This is with respect to the Elitzur–Vaidman bomb-tester. Where the of wavefunction of photon is going to collapse is not known accurately. It is said that a given photon takes both paths in the Mach-Zehnder interferometer and MAY collapse if it meets an obstacle (Bomb). few questions: 1...

Hi all, I've been doing a lot of thinking and I was wondering precisely how the 2nd order correction to the wave function from perturbation theory is derived: I mean, I can see where bits and pieces come from and I've tried to work through it as an exercise. Does anyone have a...

Homework Statement If <x> and <p> are the expectation values of x and p formed with the wave-function of a one-dimensional system, show that the expectation value of x and p formed with the wave-function vanishes. The wavefunction is: \phi(x)=exp(-\frac{i}{h}\langle p\rangle x)\psi(x+\langle...

Show that the expectation value of Lz is -2h for the radial wavefunction Y2,-2. ? Can someone do this?

Can someone help me with this problem? show that the angular wavefunction Y1,1 is a solution to the schrodinger equation.

Hi guys, Quantum mechanics gives well-defined probabilistic predictions for the value we get when we measure position or momentum; one simply takes the absolute square of the wavefunction in either the x-basis or the p-basis. However, I am not so clear on how we would predict at what time we...

Homework Statement Calculate the expected value for r^2 for the 2s wavefunction of the hydrogen atom (only the radial part of the function is needed for l=0). If you choose to solve this problem graphically, plot or sketch the function you integrate. Homework Equations...

Hi, I'm about to go into my 4th and final year of my undergraduate physics degree and after all the quantum mechanics we've done so far, I still get this nagging feeling that I'm answering homework and exam problems blindly. Apologies for the length of this question by the way. For example...

First time I learned this, I just memorized it, but now when I think about it, it seems so arbitrary. Is there a reason on why it is? And isn't it true that wavefunction cannot be...observed? In that case how can we be sure that this statement (the title) is true?

Okay, let me begin by saying that I do NOT have a good foundation in quantum mechanics, but I have been completely captivated by the wavefunction collapse. I have looked over many explanations of the double-slit experiment over the course of a few months, and I cannot find that one single...

I am very sorry that I did not use latex here. It didn't seem to be functioning properly, but I tried to make this readable. Homework Statement The wave function for a particle moving in one dimension is Psi(x, t) = A x e^[-(sqrt(km)/2(hbar))*x^2] e^[-i*sqrt(k/m)*(3/2)*t] Normalize this...

How much time does it take for wavefunction to start re-evolution after its observation is over? Or how does it evolve? I think, considering feynman path formulation, it should start evolving instantaneously, with wavefunction ending at edge of light cone (light cone that has its tip at the...

The question is the following: At one instant, the electron in a hydrogen atom is in the state: |phi>=sqrt(2/7) |E_2,1,-1,+> + 1/sqrt(7) |E_1,0,0,-> - sqrt(2/7) |E_1,0,0,+> Express the state |phi> in the position representation, as a spinor wavefunction How am I supposed to do this...

Hi, hopefully this is the right board to ask this on. I'm currently reading Groups, representations and Physics by Jones, and trying to get my head around induced transformations of the wavefunction. The problem is I seem to understand nearly all of what he's saying except the crucial part I...

I found this passage interesting and illuminating: (from Feynman's book 'QED') ".. In this example, complex numbers were multiplied and then added to produce a final amplitude for the event, whose square is the probability of the event. It is to be emphasized that no matter how many...

hi guys, two questions for today one real quick one (the velocity of waves), and one I need help on how to calculate velocity for wave function of waves. Homework Statement 1) a ocean weave with a wavelength of 120m are coming in a a rate of 8 per minutes, what is the speed. 2)The...

My lecturer writes: The spin wavefunctions are symmetric on exchange of spins for the spin 3/2 states. These states include: |\uparrow \uparrow \uparrow \rangle and |\uparrow \uparrow \downarrow \rangle + |\uparrow \downarrow \uparrow \rangle + |\downarrow \uparrow \uparrow \rangle...

Homework Statement I've attached my past paper question, which contains the relevant integral identity too. The Attempt at a Solution This question is relatively simple, yet I can't seem to complete it. I used the schrodinger equation which is: -(ħ²/2m)\nabla^2u + Vu = Eu...

So, rookie question, I know, but I'm having a little trouble with the idea of wavefunction collapse as it pertains to stationary states: If a measurement of energy collapses a wavefunction into an energy eigenstate, it stays there forever (unless perturbed). But my impression is that although...

1. What is c? 2. 1 = integral of wavefunction2 from -infinity to +infinity 3. From the graph, the area above the x-axis is 2/3 the total area. I solved the following integral (int) from -1 to +1: 2/3 = int(c2dx) Obtaining 2/3 = 2c2 So c = sqrt(1/3) = 0.58 nm-1/2

The normalised wavefunction for the 1s electron in the hydrogen atom is ψ=(1/((PI^1/2).a^3/2)).exp(-r/a) where a is the bohr radius. What is the mean value of (1/r2) in terms of the Bohr radius a0? Answer: 2/(a^2)

Homework Statement Show that the (1 0 0) and (2 0 0) wave functions of hydrogen atom are properly normalized. Homework Equations I know that (n l ml): (100) = (2/a^(3/2)) exp^ (-r/a) (200) = (1/((2a)^(3/2))*(2-r/a) exp^(-r/2a) The Attempt at a Solution I started with...

Do we have to use normalised wavefunction to calculate the expectation and probability of finding the particle? If yes, why?

Hey Guys, I'm getting a bit confused on the dimensionality of the wavefunction. I've seen the wavefunction described as: (1) A vector of norm 1 in a finite dimensional Hilbert Space (2) A vector of norm 1 in an infinite dimensional Hilbert Space (3) A continuos function (it is my...

Homework Statement at t=0 a particle is described by the eigenfunction Ψ(x) given by: Ψ(x)= iAe^(-x/2) given that x≥0 and 0 given that x<0 where A is a real number. assuming the system is in a well defined eigenstate with total energy E, write an expression for the corresponding...

Hi there, I'm not extremely adept at understanding what I like to think of as the "Philosophical" side of QM but I find I have a problem with some aspects of an interpretation of the wave function collapse. I also could be misunderstanding what people are saying. When people talk about...

Homework Statement 2 electrons are in a box of length L. Ignoring Coulomb force, 1 and 2 are labels for the electrons and m is the mass of an electron. What is the ground state and 1st excited state for the energy and wavefunction for the two electrons? Is there more than one wavefunction...

Homework Statement Take the Schrodinger equation for a point particle in a field: i\hbar \frac{\partial \Psi}{\partial t} = \frac{1}{2m}(-i\hbar\nabla - q\vec{A})^2\Psi + q\phi\Psi I'm supposed to determine what the transformation for Psi is that corresponds to the gauge transformation...

Hey guys, I have a question regarding solving a radial wavefunction DE which i have written up in Mathematica and saved as a pdf http://members.iinet.net.au/~housewrk/PFpost.pdf" as I was already doing the work in MM and writing it all up again in LaTeX seemed a bit of a waste of time. If...

I'd like to know why wave functions are taken to be complex-valued in general, and where the i in the Schrödinger equation comes from and what it means. I've seen plenty of we-use-this-because-it-works type arguments. What I'm hoping for is a meaningful explanation of how the complex numbers...