Wave function Definition and 878 Threads

Homework Statement http://www.whoisntdavidrinaldi.com/Untitled.png Homework Equations The Attempt at a Solution So I had to use this initial momentum and multiply it by a plane wave (sure you are aware of the exp[i(px+p^2(t)/2m)\hbar] ) setting p-p_0 to q and then coupling all terms...

Hello! So as you all know the wave-function can be expressed as: y(x,t) = A\cos(kx-\omega t) However, this can be interpreted as both a standing and moving wave. So when do you interpret it as either of those? Are there any special conditions that should be written along with the wave function?

Homework Statement ψ(x,t) = Ae^(-λ|x|)e^(-iωt) This is a rather long problem so I won't get into the details. I understand how to normalize, and most of the rest of the problem. I also have the solutions manual. I just need an explanation of why this goes to Ae^(-2λ|x|). I can't figure it...

Homework Statement \psi (x) = Ne^{ \frac{-|x|}{a}+ \frac{ixp_o}{/hbar}} Compute Fourier transform defined by ##\phi (p) = \frac{1}{ \sqrt{2 \pi \hbar}} \int \psi (x) e^{ \frac{-ipx} {\hbar}} dx## to obtain ## \phi (x) ## Homework Equations Fourier transform = ##g(x)= \frac {1}{2 \pi} \int...

Homework Statement A particle is moving in one dimension in a potential V(x,t). The wave function for the particle is... and then the equation is given.. Show that V is independent of t, and determine V(x). Homework Equations The Attempt at a Solution I don't know where to...

wave function always refer to the position of particle with probability amplitude. since wave function is not a wave but field, frequency seems meaningless to it. can i imagine it is a vibration field with certain frequency f in complex plane or something?

In flat spacetime, there isn't any problem with wave function collapse. I think that's the "textbook" position, although the only citation I have off the top of my head is the discussion in http://arxiv.org/abs/0706.1232 (section 1.1). How about in curved spacetime (working in the regime where...

A particle in the infinite square well potential is found at the 3-rd excited state. What is the wavelength of the wave function of the particle? this is a mcq from my faculty who denoted the correct answer to be 2/3 a ...how to get that ?

I am trying to develop a graphical, interactive simulation of a wave function in position space, given an arbitrary potential. It works great, but as a final touch, I would like the user to be able to collapse the wave function, either by measuring its position or its momentum. My problem is...

Hi I am currently looking for the wavefunction of the bonding orbital of the hydrogen molecule. Does anybody here know how this one might look like? So, since there is no complete analytical solution for the Hydrogen atom Schrödinger equation, I am currently looking for approximations of this...

hi, i read in quantum mechanics wave function is a combination of eigenfunctions and according to Orthodox interpretation measurement causes the wave function to collapse into one of the eigenfunction of the quantity being measured. Is this explanation still valid?

hi, please explain can by using suitable operator we can find any physical quantity- as by using hamiltonian on wave function we can find energies by the eigenvalues? thanks wasi-uz-zaman

I'll write down what i know and point it out if I'm wrong.So we normalize the wave function because -∫|ψ(x,t)|^2dx should always be equal to 1 right? Has this anything to do with transition from ψ to ψ^2?

Apologies if these questions have been answered before - I didn't have any luck with google. Something has bugged me for a while about quantum experiments like Schrödinger's cat where a 'black box' system is theorized to be in a superposition of states until observation causes wave function...

Homework Statement So I have this normalized wave function psi=sqrt(2/a) * sin^2(pi*x/a) with limits of 0 and a. I'm supposed to find the probability for a bunch of points if this form: p(x=0.00a,x=0.002a) Homework Equations P(a,b)=int(psi^2)dx The Attempt at a Solution...

We know that electrons are nearly massless so their wave funtion is quite easily detectable.So is there any mathematical relation between the mass of the body and the intensity of the wave it exhibits? thanks

Homework Statement The following picture is supposedly periodic (or at least my teacher says so). Could anybody suggest where I begin in order to determine the wave function for this messy graph. Please see the attached for the graph.

Homework Statement Hello, I have this problem with seemingly simple process, but there are things I either don't know, or make some stupid mistake on the way over and over. Here's the problem: At a particular time given by the wave function ψ(x)=N*x*exp(-(x/a)2) Determine N so that the wave...

Hello everybody, I am currently struggling with a problem that I came across while spending some free time on non-relativistic quantum mechanic problems. Suppose we have an electron that is describe at time t_0 = 0 by a wave function in position space \psi(x,y,z). Furthermore, assume...

In the cellular method of calculating the band structure: Why we have to take zero the normal derivative of the wave function at the Wigner-Seitz cell's border?

Homework Statement Prove the following theorum: The time-independent wave function ## \psi (x) ## can always be taken to be real (unlike ##\Psi (x,t) ##, which is necessarily complex). This doesn't mean that every solution to the time independent Schrodinger equation is real; what it says is...

Homework Statement A particle of mass m is in the state ψ(x,t) = Ae-a[mx2/h-bar)+it] Find A Homework Equations I know that to normalize a wave function I should use ∫ψ2 = 1 The Attempt at a Solution The book gives the solution as 1 = 2abs(A)2∫ e-2amx2/h-bar) dx My question is...

Homework Statement A particle of mass m is inside a 1 dimensional "box" of length L such that it's restricted to move between ##x=-L/2## and ##x=L/2## where the potential vanishes. 1)Determine the eigenvalues ##E_n## and the eigenfunctions ##\psi _n## of the Hamiltonian imposing that the...

Hello guys, problem is as follows: X9) A free electron has energy (kinetic) 10 eV and moves along the positive x-axis. a) Determine the electron's wave function. b) The electron reaches a potential step,-V0. Determine V0(expressed in eV), so that the probability of reflectance is 25%. c)...

Homework Statement Two-electron Wavefunction: ψ(r1,r2,r12) = exp(-Ar1-Br2-Cr12), r12 = |r1-r2| A, B, and C are coefficients Calculate <ψ|δ(r12)|ψ> and <ψ|δ(r1)|ψ> Homework Equations NO The Attempt at a Solution <ψ|δ(r12)|ψ> = ∫∫dv1dv2ψ2(r1,r2,r12)δ(r12)...

Wave function is a complex number , why do we have to consider it as a complex number? Quote:– but there is nothing in the wave equation that restricts them to being real numbers. If we temporarily suspend disbelief that physical quantities may be associated with complex amplitudes, then we...

Elementary question: When one talks of a wave function of a measured object collapsing or decohering or splitting (pick your interpretation), what we base everything on is the measuring pointer. So, which of the following is the case? (a) one calculates with help of coupling constants etc...

Homework Statement Normalize the wave function ψ(x,0) = C1/4 * ea(x2)-ikx a and k are positive real constantsHomework Equations ∫|ψ|2dx = 1The Attempt at a Solution Now, my maths is a little weak, so I'm struggling a little bit here. The constant is easy to deal with in all aspects of...

Homework Statement At time t = 0 a particle is described by the 1D wave function ψ(x,0) = (2α)^1/4 e^-ikx-α Verify that this is normalizedHomework Equations Er! I have just started this sort of thing, so just a bit confused. I think I can do this if there are limits as to where the particle is...

Homework Statement Suppose a Gaussian wave packet ψ(x,0) is built out of plane waves according to the amplitude distribution function A_{k} = \frac{Ca}{\sqrt{\pi}}e^{(-a^2(k-k_{0} )^2)} Calculate ψ(x,t) for this packet and describe its evolution. Homework Equations ψ(x,t) =...

For a wave function describing the state of an isolated system in 1D, does a wave function describe a system completely?

Homework Statement For the n = 1 harmonic oscillator wave function, find the probability p that, in an experiment which measures position, the particle will be found within a distance d = (mk)-1/4√ħ/2 of the origin. (Hint: Assume that the value of the integral α = ∫01/2 x2e-x2/2 dx is known...

|ψ(x,t)|2 is the probability density. Probabilities are dimensionless. What would the SI units of |ψ(x,t)| be, then? Also dimensionless?

Problem: Which of the wave functions shown might conceivably have physical significance? Solution: I have attached a drawing of the two wave functions. According to my book, the one on the right could have physical significance, while the one on the left does not. Can anyone explain why not...

Just starting QM & am looking at TISE & how it builds from start & need a little help understanding. OK, for a free particle the de Broglie wave function is ψdB(x,t) = Aei(kx-ωt) where A is a complex constant this corresponds t a free particle with momentum magnitude p = h/λ = hbar k...

Homework Statement You have the simple harmonic equation for a transverse wave which is y(x,t)=Acos(10∏t+5x), what is the wave function at the originThe Attempt at a Solution By "at the origin" does it mean where x=0 and t=0. Because it that case y=Acos0 and therefore y=A. Is that right?

I have been searching for an anwser everywhere, but i can't seem to understand something. In this topic (you don't need to read it) i managed to find out that "we can calculate normalisation factor ##\Psi_0## of a wavefunction ##\Psi## if we integrate probability ##|\Psi|^2## over some volume...

What is the wave function of a simple harmonic wave? y(x,t)=Asin(ωt+kx)

I don't want to argue about whether the notion of "wave function collapse" is a good way of understanding quantum mechanics, or not. For the purposes of this discussion, let's just adopt uncritically the naive approach to quantum mechanics, that: Between measurements, the system evolves...

Hi First I should point out that I don't have any scientific knowledge in Quantum Mechanics. I am just enthusiast physicist not professional. I am interested in physics and the only thing that I know for now is Classical Mechanics (Newtonian, Lagrangian and Hamiltonian reformulations) and some...

I'm doing about wavefunctions for my course, I'm a bit confused as to why the wavefunction of Helium has 9 coordinates and time and not 6 coordinates and time. As far as I was aware the wave function was used to describe the movement of electrons around the nucleus of an atom, and it was assumed...

A friend of mine recently tried to tell me that the square of the wave function for a particle (that is, \Psi^2) gives the probability density of finding a particle in space. I disagree. I always thought that the wave function multiplied by its complex conjugate (that is, \Psi \Psi^*)...

Hi, I've done a lot of personal research on the internet trying to understand what exactly is happening in this experiment but I keep seeing contrasting information about what the role of observation actually had on the experiment. What I understand is that when they try to figure out which...

I can not seem to find out what a wave function function is amd I would just like a simple explination of what it is and how it is used. And what is this symbol ψ. Thank you.

I hear some reasons that photon exist in 4D space-time, wave function not and so on. But, an electron can be described with de Broglie waving and we can use wave function to describe electron. Frequency of the wave function is the same as energy/\hbar and k of wave function is the same as...

I was trying to understand wave function collapse in terms of superposition, but I ran into some problems when relating back to information theory/entropy. It is given in the definition of information in terms of entropy energy is needed to transfer information. That is something we have always...

Homework Statement A particle is in the state 1/2 |1> - 1/2 |2> + 1/2 |3> - 1/2 |4> A detector is placed to measure state |4>. What the particle's wave function collapses into, if the detector does not find a particle Homework Equations <i|j> = delta (i, j) The Attempt at a...

Homework Statement A particle in the infinite square well has its initial wave function an even mixture of the first two stationary states: \Psi(x,0) = A\left[ \psi_1(x) + \psi_2(x) \right] Normalize \Psi(x,0). Exploit the orthonormality of \psi_1 and \psi_2 Homework Equations \psi_n(x) =...

As I understand it the wave function itself does not carry any physical interpration. Rather it is the square of it's absolute value. But that forces the question: Why construct a theory with the basic equation being about the time evolution of the wave function, when you could (I guess just as...

When dealing with n-particle systems that are identical, is the superposition of them just a mathematical construct, or is it similar to how the state of a single particle can be in multiple eigenstates until its measured. For instance, if I have two fermions: \Psi = \Psi_a(x_1)\Psi_b(x_2) -...