Wave function Definition and 865 Threads

I was reading part of a book which was explaining about the probability of finding a particle on a 1d line. \int^{+\infty}_{-\infty}P(x) dx = 1 This sounds right because if the line was infinitely long then the particle must be on it. You can them intergrate between a and b to find the...

Homework Statement a particle moving in one dimension between rigid walls separated by a distance L has the wave function \Psi(x)=Asin(\Pix/L), since the particle must remain between the walls, what must be the value of A? Homework Equations The Attempt at a Solution Ok so I'm...

As far as I understand it, an electron exists as a probability cloud around an atom, representing all the possible places it could be. Then when we make an observation the wave function collapses to one point where we see the electron. So what happens if we keep looking at it? Does the elctron...

Homework Statement Knowing: y(x,t) = Acos(kx-ωt) Find the partial derivatives of: 1) dy/dt 2) dy/dx 3) d^2y/dt^2 4) d^2y/dx^2 Homework Equations The Attempt at a Solution These are the answers the actual answers: 1) dy/dt = ωAsin(kx-ωt) = v(x,t) of a particle 2) dy/dx =...

the double slit experiment is explained in QM as the superposition of two wave functions. Each is the wave function for one of the slits. an electron starts out with a wave function that is clustered near the point of emission and then evolves on some way according to the Shroedinger...

Homework Statement Hi guys, I'm really confused about how to about solving this problem, any help would be much appreciated. Consider the wave-function: \Psi(x,t)=\left\{\begin{array}{cc}Asin(pi*x)\exp^{-it\omega},&\ -1\leq x\leq 1\\0, & \ elsewhere\end{array}\right{ a) Determine A...

Here's the sitch: I am given an equation, A*e-a(mx2/h-bar+it) I need to find the value for A that will satisfy normalization, as well as find the Potential of the Schrödinger Equation using this value. What do I do? P.S. I have NOT learned gaussian integration, which is where I run...

Homework Statement Come up with a wave function Psi[x] that satisfies the given known values: <x>=-1 sigma x = 1 <p> = h bar Homework Equations The Attempt at a Solution So far I have this equation, which satisfies <x>, <p>, but not sigma x. 1/[Pi]^(1/4) E^(i (x + 2)) E^(-(1/2)...

Homework Statement Hi all. I have a wave function given by \Psi \left( {x,0} \right) = A\frac{x}{a} I have to normalize it, which is OK. But in the solution to this problem, the teacher uses |A|2 when squaring A. Is there any particular reason for this? I mean, if you square the constant...

Homework Statement Check that a given momentum space wave function is normalized. I've done the integral, but the result is not dimensionless. Here is the wave function: \overline{\phi} = \frac{1}{\pi} ( \frac{2 a_{0}}{\bar{h}})^{3/2} \frac{1}{(1+(a_{0} p / \bar{h})^2)^2} The units of this...

I believe it does, but I'm having a debate with someone and I'm trying to prove why the universe must have a wave function. I was under impression the best equations for describing our universe involve it having it's own wave but he's asserting it doesn't need one. Can anyone help me? Super newb...

I believe it does, but I'm having a debate with someone and I'm trying to prove why the universe must have a wave function. I was under impression the best equations for describing our universe involve it having it's own wave but he's asserting it doesn't need one. Can anyone help me?

What is exactly a wave function of the system. I have been told that wave function is something that is used to describe the wave nature of a particle but how? I could not understand or rather visualize it. And how can the wave function be a complex number or a negative value? For example if...

what is it that actually collapses a wave function, an observer? what constitutes an observer? also is it true that everything has a wave function, because if it does who collapsed the universes wave function some may say wave function collapse only works on the quantum level but the universe...

Hi, I've been working on writing the wave function in terms of momentum eigenfunctions. The only problem I have with the derivation is the last step, which allows me to write: \Psi(x) = \int^{\infty}_{-\infty} \phi(p)u_{p}(x)dp where u_{p}(x) =...

Its looking quite simple problem but let me explain properly my question. Wave function as we know is also known as matter wave/field amplitude. Then definitely there is associated a wave with it. Then how can we say that wave amplitude vanished at infinite!

Problem We have the function g(x)=x(x-a) \cdot e^{ikx}. Express g(x) in the form \sum_{n=1}^\infty a_n \psi_n (x) where \psi_n = \sqrt{\frac{2}{a}} \sin \(\frac{n\pi x}{a}\) Solution I have absolutely no clue as to how to start... I know a bit about Fourier series, but here, the...

how to tranform wave function(x,t) to same coordinate wave function(x',t') with Lorentz Tranformation (please show all the calculus). and why we know the Lorentz tranform can do this function to use in every inertial frames.

Homework Statement Does the wave function have a dimension? If it does, what are the dimensions for 1D and 2D box problems?Can you generalise this to n dimensions? Homework Equations The Attempt at a Solution Yes, it does have dimensions. For 1D box it's [tex] m^{-2} [tex]...

Hi, could someone please tell me how I would show that a wave function is correctly normalised? I know to integrate the square of the function between infinity and negative infinity, but is the complex conjugate required? Any help is much appreciated :D

Hi everyone, Can anybody solve my simple problems of quantum: Usually we say, that wave function Ψ is dependent on r,θ,Φ .But this is just a coordinate system,or more than that. Imagination to this is qite difficult. Moreover somewhere in a book I have read that if Ψ = f(r,θ) exp(imΦ),then on...

Homework Statement A particle of mass m is in the ground state of the infinite square well. Suddenly the well expands to twice its original size, the right wall moving from a to 2a- leaving the wave function (momentarily) undisturbed. The energy of the particle is now measured. What will be the...

I read in my textbook that the wavefunction of a particle evolves causally when unobserved. but isn't it constantly being observed or detected in some sense by its gravitational effects?

Homework Statement I am having a problem with an example problem in my physics book. The example goes like so: a.)Show that \psi(x) = Ax + B A, B, constant is a solution of the Schrodinger equation for an E = 0 energy level of a particle in a box. b.) what constraints do the boundary...

Does anyone know how to construct a Time-independent wave function with given energies and probability on obtaining energies.

Homework Statement Construct wavefunction with given energies and probabilities of obtaining energies in a 1-D box from 0 to aHomework Equations [b]3. The Attempt at a Solution I know the general form of a time-independent wavefunction but I don't know what to do with the probabilities of...

For a particle in a 1-dimensional box confined by 0<x<a. a)Construct a wave function phi(x)=psi(x,t=0) such that when an energy measurement is made on the particle in this state at t=0, the following energy values are obtained with the probabilities shown: Energy E_n Obtained ...

Can a quantum wave function be infinite at a point? For example you could have a radially symmetric wavefunction that's infinite at the center, yet the integrated probability is 1. Is this unphysical somehow? Laura

[SOLVED] Wave Function Solution Homework Statement An electron is found to be in a state given by the wave function http://rogercortesi.com/eqn/tempimagedir/eqn7955.png Find the value of A. Homework Equations The normalization of the wave function...

[SOLVED] Probability Current for Free Particle Wave Function Homework Statement Find the probability current, J for the free particle wave function. Which direction does the probability current flow?Homework Equations J(x,t) = \frac{ih}{4\pi m}\left(\Psi \frac{\partial \Psi^{*}}{\partial x} -...

does a phase factor (that can be represented by an imaginary exponential) in psi (the wave function) really matter? I am doing a problem and getting an answer that looks like sin[n(pi)x/a] when the answer is actually sin[n(pi)x/a-n(pi)]. I am just wondering at all if it makes any defference in...

Homework Statement Show that y(t-x/v) is a solution of the wave equation without taking any partial derivatives (hint: use your knowledge about f(x-vt)). Homework Equations y(x,t)=y(x-vt) The Attempt at a Solution what exactly is y(t-x/v) means, from dimension analysis, its the...

hello I am just starting some revition for my exams and havr come across this wave funchion and i don't no how to normerlise it i really need some help with this. it is the wave function symbol (x) = -Ae^(σx^2/x^2) what i need to know is how to intergrate it to find a value for A to see if...

Reading Sam Treiman's http://books.google.de/books?id=e7fmufgvE-kC" he nicely explains the dependencies between the Schrödinger wave equation, eigenvalues and eigenfunctions (page 86 onwards). In his notation, eigenfunctions are u:R^3\to R and the wavefunction is \Psi:R^4\to R, i.e. in contrast...

I have a wave function problem that I need to figure out... I have a really borderline grade, so it could mean the difference between an 'A' and a 'B' in my graduate Modern Physics class. Basically, I have to figure out the wave function and the transmission and reflection coefficients. My...

Homework Statement P = \int_a^b \, \left| \psi(x) \right|^2 \, dx If the particle in the box is in the second excited state (i.e., n=3), what is the probability P that it is between x=L/3 and x=L? To find this probability, you will need to evaluate the integral: \int_{L/3}^L...

Homework Statement Open Question 2.bmp Homework Equations The Attempt at a Solution Open Answer 2.bmp I really struggled with this one, my answer is nothing more than an incomplete educated guess.

Hi all, How do we find the eigenfunctions if we are given the wavefunction? I have a wave function at time = 0 and it is of a *free* particle and I need to find the wave function at a later time t. I did : \Psi(x,t)=\Psi(x,0)*e^{-iHt/hbar} then \Psi(x,t)=\sum_{n}(<\phi_{n}|\Psi(x,0)>...

Hello, How do I find the normalization constant for psi(x,y,z) = N exp -(x/2+y/2+z/2) ?? I did the following: \int(psi^* psi)dx dy dz = 1 the integral bounds are from -infinity to infinity and the * means the complex conjugate.The integral is so weird that I couldn't find N. I used...

Homework Statement At t=0, the particle is in the eigenstate S_x , which corresponds to the eigenvalues -\hbar \over 2 The particle is in a magnetic field and its Hamiltonian is H=\frac{eB}{mc}S_z . Find the state at t>0. Homework Equations Eigenstate of the Sx is...

Homework Statement Find the momentum-space wave function, \Phi (p,t), for a particle in the ground state of the harmonic oscillator. What is the probability (to 2 significant digits) that a measurement of p on a particle in this state would yield a value outside the classical range (for the...

I need to normalize the following wave function: psi= Cexp(-abs(x))exp(-iwt)cos(pix) I know that when squaring it, the time dependent part drops out, which is good, but what I seem to be left with is Psi^2=C^2exp(-2abs(x))cos^2(pix) Which seems like a fairly complicated integral to...

Hi all, I've got a question I think I understand conceptually but not mathematically... Homework Statement A transverse sinusoidal wave on a string has a period T = 25.0 ms and travels in a negative x direction with a speed of 30.0 m/s. At t=0, a particle on the string at x=0 has a transverse...

I want to know whether the wave function of particle is unique? If not, could we find a ψ to rationalize the equation Pψ=Aψ, in which P is the momentum operator and A is a constant. Thank you!

XXZ model in 1-dimension, with external field, what is the exact form of its ground state wave function? Recently I've read the ground state wave function of XY model and was curious about the condition of XXZ. Do they have a similar manner? The XY result is attached below. Thanks.

Homework Statement Hi all, I've been given some homework on wave functions to find direction and velocity etc... but as its the first week of uni for me, we haven't even covered wave functions or anything :/ and the homework is due on weds 10th oct... Homework Equations...

I've heard some people say that the wave function and its first derivative must be continuous because the probability to find the particle in the neighborhood of a point must be well defined; other people say that it's because it's the only way for the wave function to be physically significant...

Homework Statement Just a snipit of one of my homework problems. I'm trying to find out what \Psi \frac{\partial \Psi^{*}}{\partial x} equals to help me find out what the probability current for a given free particle is. Homework Equations \Psi = Ae^{i(kx-\frac{\hbar k^{2}t}{2m})}...

why is not need for introducing a true collapse in bohmian interpretation?

Why is it that when observing an electron or photon it causes the wave function to collapse, surely the photons that cause this collapse were still "colliding" with it when we wern't looking. Or does it only collapse the wave function from the observers viewpoint? (I'm abit of a noob so if...