Wave function Definition and 878 Threads

Homework Statement Prove that the spherical harmonic wave function \frac{1}{r}e^{i(kr-{\omega}t)} is a solution of the three-dimensional wave equation, where r = (x^2+y^2+z^2)^{\frac{1}{2}} . The proof is easier if spherical coordinates are used. Homework Equations Wave function...

Hi, I have been looking for explanation,how to draw angular part of wave function and I have found in physicsforums.com/archive answer to my question by user Gokul43201. He posted this: The trick is in being able to draw polar plots roughly, from the spherical harmonics. Consider the...

Homework Statement In a book I found the following calculation without the way. How do you get from 1) to 2)? Homework Equations (1) \Psi(x,t)=\frac{A}{2\pi}\sqrt{\frac{\pi}{d²+i\frac{\hbar t}{2m}}} exp{\frac{-\frac{x²}{4}+id²k_{0}(x-\frac{k_{0}\hbar}{2m}t)}{d²+i\frac{\hbar t}{2m}}}...

I'd like to get some help and pointers on how to derive a wave function. Since I'm not really good at physics I'm just going to use brute force, if anyone spot a mistake please please point it out. If I look at an electron in an well with infinite potential walls. The well has the dimensions...

in a double slit experiment, if we find which-way and then stop observing the photon and send it again through another double slit (kept in, say, series), would an interference pattern occur?...the second time around

Homework Statement Using the results of the previous problem, find [x,p2 ] and from that determine [x,p2 ]\psi(x) Homework Equations The solution to the previous problem was [A,BC]=[A,B]C+B[A,C] The Attempt at a Solution As I'm suppose to use the results of the previous problem I...

Homework Statement Consider the wave described by: E= 3 sin [pi (x/c - t)*10^13+ pi/6] True or false? 34. The frequency = 10E13 Hz. 35. The wavelength = 3E-6 m. 36. The direction of motion: positive x direction. 37. The speed = 300 000 km/s. 38. The maximum amplitude = 9...

Hello again! Say I have a potential well, between 0 and a. I also know how the wave function looks like for (t=0): \psi(x,0)= \frac {2bx} {a} for 0<x<\frac {a} {2} and \psi(x,0)= 2b(1- \frac {x} {a} ) for \frac {a} {2} <x<a Now, I wish to find the wave function of a general time...

Consider a super cold gas tube (of, say, hydrogen), is the wave function of the gas different than at a higher temperature? How about for a lone electron within the gas?

Hello! There is something I can't understand... \psi(0)= \frac {1}{\sqrt 5}|1>+ \frac {2i}{\sqrt 5}|2> I need to find <H> for \rightarrow \psi(t) For E_n= \hbar \omega (n + \frac {1}{2}) , \hat {H} =(a^\dagger a+1/2) These make me understand that this problem is one dimensional. (+1/2 in...

Let's say an observer A in his rest system has a wave function for an electron double slit experiment (psi function of x and t). Would there be any inconsistencies between QM and relativity coming out of a QM analysis performed by observer A and some other observer, B, who is moving at...

Hello physicists, My question is why a wave function has to be 0 at infinitiy. The author who I was studying him quantum book explains my question by saying that it is necessary to make wave function normalizable. But in my opinion there can be an arbitrary particle which can be found all...

Homework Statement I don't know how to prove b.) Homework Equations The Attempt at a Solution What can I do after writing these 4 eqtn?

ψ(x) = A/(x - ik) over the region x = -∞ to ∞ A and k are constants, and i is √-1. I'm not sure if this is a valid wave function or not. I know that ψ must be continuous "everywhere," but this function does not exist for x = ik. But x only takes on the form of real numbers over the interval...

I’ve been fascinated with the different QM interpretations since I discovered them… but I want to sort of restrict my imagination to more solid ideas. I know about the Double-Slit experiment and that there are many misconceptions about the correct definition of an ‘observer’ and what role the...

Hello: I know it's a rather subjective title. But I am no expert in the subject and I've read a lot of information in the Internet that is contradictory. I have read that the collapse of the wave function requires interaction with an observer. But is that collapse in any way related to the...

I want to calculate the momentum of the wave given by psi = Asin(8.92e10 x) where x is in metres. I know that momentum = planks/wavelength, but I'm unsure of how to get any information out of the wavefunction alone... any guidance would be appreciated. mitch

Hello! I'm preparing for my quantum mechanics test. In the solutions of an old test I find this conversion, that I don't understand. \Psi = Nze^{-r/2a_0} = Nre^{-r/2a_0}cos\Theta N is the normalization constant, which is to be calculated. I would have guessed that z is the atomic...

Hi! I have a plan to build my own version of young's experiment using various household items, a laser, and my physics textbook. My question is about what I could use as a "detector" to observe and collapse the wave function? I had the idea of making a tiny inductor to go around one of the...

Someone told me that in the experiments which display the collapse of the wave function, there is no need for a conscious observer. They said if we left an observing instrument on its own it would manage to do the same thing. Is this true? In fact this person thinks that the instrument...

A simple, harmonic oscillator at the point x=0 generates a wave on a rope. The oscillator operates at a frequency of 40 Hz and with an amplitude of 3.00 cm. The rope has a linear mass density of 50.0 g/m and is stretched with a tension of 4.50 N. Write the wave function y(x,t) for the wave...

Homework Statement A wave packet is described by the momentum-space wave function A(p)=C when 0<p<p0, and A(p)=0 for all other values of p. Here C is a constant. i) Normalize this wave function by solving for C in terms of p0. ii) Calculate the expectation values <p> and <p2>. From...

I think all the confusion and arguments of what is measurement in quantum mechanics can be boiled down to what really is a wave function. My head is spinning for a week thinking all about it and the following organize my thought about it. Correct me if I'm wrong and where I'm wrong in the...

What are these oscillations in a coherent superposition? A guy called Chalnoth stated in the Cosmology forum: I don't know if he states this because of bias (he is a Many World interpretation believer). That's why I'm asking this here. He states dynamics can't occur in a superposition...

Homework Statement for a wave function confined between x=0 and x=L find an expression for A in order that the wave function be normalized The Attempt at a Solution for a particle in a box between 0 and L the normalized wave function is integral of C2sin2(n\pix/L).dx = 1 using trig...

Homework Statement how do I take the real part of y2= A exp (4ix) exp (-2it)? And how does this determine that this wave propagates with constant speed compared to these wave disturbances: y1= A sin (5x) exp (-2t) y3= A sin (2x-5t) exp (-2t) Homework Equations exp(ix)=...

I just start to study quantum mechanics and i don't understand why square of wave function is probability density function. I think the reason of taking square of wave function is because we should eliminate complex compounds of wave function to get a real magnitute. But after why don't we take...

hi guys, i wanted to know what the wave function exactly mean?and what is the physical interpretation of wave function?

Homework Statement Find the wavefunction for an infinite well, walls are at x=0 and x=L(include the time dependence) The Attempt at a Solution I don't understand what it's meant by include the time dependence. Can I just find the time-independent wavefunction and then multiply it by...

Consider a hydrogen atom whose wave function is at t=0 is the following superposition of energy eigenfunctions nlm(r) (r, t=0) = *[2100(r) -3200(r) +322(r) What is the probability of finding the system in the ground state (100? in the state (200)? in the state (322)? In another energy...

Consider a hydrogen atom whose wave function is at t=0 is the following superposition of energy eigenfunctions \psinlm(r) \Psi(r, t=0) = \frac{1}{\sqrt{14}} *[2\psi100(r) -3\psi200(r) +\psi322(r) What is the probability of finding the system in the ground state (100? in the state (200)? in...

Ever two-particle wave function is a product of two one-particle wave functions. Is this true? if not, can you give me a example ? Thank you :)

Hi there My textbook says the following is the time independant wave function for a stationary state: \Psi(x,y,z,t)=\psi(x,y,z)e^{-iEt/\bar{h}} Just trying to get my definitions straight...is a stationary state the analogue of a standing wave?

Homework Statement To find the stationary states and the corresponding energies, I need to normalize the following equations: X(x)=A_x sin(\frac{n_x\Pi}{a}x) Y(y)=A_y sin(\frac{n_y\Pi}{a}y Z(z)=A_z sin(\frac{n_z\Pi}{a}z Because of their similiraty, these value of the normalize...

I can normalize wave functions all day, but I still don't know what I mean when I normalize them! So my question, what does it mean to normalize a wave function?

Whats the use of solving for the wave function of water? Or is it not solvable at all?

Homework Statement One of the quantum mechanics wave functions of a particle of unit mass trapped in an infinite potential square well of width 1 unit is given by Ψ(x,t)= sin(\pix)e^{-i(\pi^2\overline{h}/2)t} + sin(2\pix)e^{-i(4\pi^2\overline{h}/2)t}\ where \overline{h} is a certain...

Homework Statement [PLAIN]http://dl.dropbox.com/u/14655573/110218_203248.jpg Part (1) The figure shows the output from a pressure monitor mounted at a point along the path taken by a sound wave of a single frequency traveling at 343 m/s through air with a single frequency traveling at...

Homework Statement Given \Psi(x,0)=\frac{A}{x^{2}+a^{2}}, (-\inf<x<\inf) a) determine A c) find the momentum space wave function \Phi(p,0), and check that it is normalized Homework Equations At t=0, we can find the momentum space wave function by the formula...

The wave function is complex. I was taught that its square (probability) was actually psi times it's conjugate. Does this relationship always hold or was this only for bound and free particles? In other words is it possible for psi and psi* to change phases during orbital state transitions?

Is it ever useful to find the Shannon entropy or information content of a wave function? Thanks.

Dear friends, I've come across this questions when studying biatomic molecules. Here's my problem: You have the following two wave functions: Psi_1 = px(A) + px(B) Psi_2 = py(A) + py(B) here px(A) is the px orbital wave function of the A nucleus, px(B) of the B nucleus and so on...

The ultimate goal of the problem is to show that the stationary state two body wave function can be written as \Psi(\vec{r_1},\vec{r_2},t)=e^{i\vec{P}\cdot\vec{R}/\hbar}\psi_E(\vec{r})e^{-i\left[\frac{P^2}{2M}+E\right]t/\hbar} So far, I have separated the variables in the time independent...

Hi, In Copenhagen Interpretation, the wave function is just a mathematical tool that has no physical reality. In Bohmian Mechanics, the wave function has objective reality as some kind of field. Why can't we have both where the wave function has objective reality as some kind of field...

Please correct me if I am wrong as I am trying to get a better grasp on this. As of now my understanding is that my bed is in my room. But according to the wave function it is also "smeared" across other spaces. Therefore my bed is also in the dining room. There is a VERY small chance but...

could the universe act like a wave that at the present time is accelerating towards a peak something akin to an electromagnetic sine wave? And once the peak is reached it starts to deflate? Could this dark energy be the alternate wave that is at right angled to the universal wave? Just musing...

I have three question regarding the electronic wavefunction \Psi Ques 1 What does value of wavefunction of any orbital signify ? Is it just a mode of calculating other quantities like probability amplitude etc. or does it have a significance in itself ? Ques 2 What does the...

I recently had a probelm in QM to find the time evolution of a hydrogen prepared in a state with a wave function that is not an energy eigenfunction: specifically, psi = Y21*R2p where Y is then the D spherical harmonic. Of course, n=2 hydrogen doesn't have d oribtals. So the problem is I...

I know this may be a completely stupid question and it's so fundamental but... As we all know the first thing we learn is basically the duality between waves and particles (e.g electron). This is shown via the double slit experiment. Now I know how to explain it if it were water waves, and...

Hi there, I have question about a gluon's wave function. First of all, I thought it is just the vector potential A_\mu but I read several papers and they keep referring to the helicity \epsilon_\mu as the wave function. At least this is what I understand from the context. See for instance...