Wavefunction Definition and 585 Threads

In QM, the wave function is a wave in hilbert space. But is it possible that it is a physical wave in physical space? I think that there are a few interpretations/theories of QM that describe it as a physical wave.

Why wavefunction (the square of its modulus) of an electron is not seen as a measure of substance/charge distribution of the electron?

Hello, please help me with normalization problem.. f is sin(Pi x/L) between 0, L first we use normalization formula and integrate N^2 Sin^2(pi x/L) to get N^2( L/2) Sin L/2 which equals to one ... this is my solution in the textbook his result is N^2 (L/2) My question is how he get rid of...

I'm alittle confused, is it saying that all the fundamental particles in the universe are really just one wave function?

Hi, I am trying to find the wavefunction of a coherent state of the harmonic oscillator ( potential mw2x2/2 ) with eigenvalue of the lowering operator: b. I know you can do this is many ways, but I cannot figure out why this particular method does not work. It can be shown (and you can find...

In a solid, is electron's wavefunciton confined to a molecular orbital between atoms or is it delocalized and extends over the volume? According to valence bond theory, electrons are localized in bonds between atoms. But according to band theory (or Bloch wavefunctions), electrons are...

I have operators satisfying ##[\hat{Z} , \hat{E}] = i \hbar##. The operators ##\hat{Z}## and ##\hat{E}## are taken to be Hermitian. You consider the unitary operator ##U_\lambda = \exp (i \lambda \hat{Z} / \hbar)##. I have proved that ##U_\lambda \hat{E} U_\lambda^\dagger = \hat{E} - \lambda...

I have poor concepts in Orbitals, wavefunctions etc. What i know is that quantum mechanics(study of sub atomic particles) talks about probability. What i understand is wavefunction means probability of finding an electron in space around a nucleus, correct me i am wrong.So when we say that this...

The modern view of the measurement problem is that any interaction of a particle (say an electron) will cause its wavefunction to 'collapse' in the process called decoherence. No need for conscious observers, interaction with any other particle will cause decoherence hence collapse of the...

Hello Guys, I am trying to Normalize the following wave function but I am getting stuck in between (Maybe maths is the problem here for me). Can anyone please provide some hints. The Wave Function is ψ = e - |x| sin (α x)Please help.

A wavefunction of a single particle (ignoring spin etc) is a three dimensional object mapping to 3-D physical space. The wavefunction of two unentangled particles is separable as a product of two independent 3-D wavefunctions. If the particles are entangled, the states cannot be separated, the...

Assuming the 2s and 2p wavefunctions are normalized, determine the coefficients in the hybrid orbital: Ψ(sp3) = aΨ(2s) + aΨ(2px) + aΨ(2py) + aΨ(2pz) (the other 3 hybrids have – signs for some of the coefficients. I have no clue where to start. I know this is a tetrahedral hybrid orbital but...

Homework Statement Consider the wavefunction ##\Psi (x, t) = c\ \psi (x) e^{-iEt/ \hbar}## such that ##\int | \Psi (x, t) |^{2} dx = 1##. I would like to prove to myself that the normalisation factor ##c## is a real number. Homework Equations The Attempt at a Solution ##\int | \Psi (x, t)...

Homework Statement For a particle of mass m in a one-dimensional infinite square well 0 < x < a, the normalised energy eigenfunctions ψn and eigenvalues En (integer n = 1, 2, 3, ...) are $$ \psi_n(x) =\sqrt{\frac{2}{a}} sin \left( \frac{n \pi x}{a} \right) \;$$ inside the well otherwise...

My question concerns a really simple differential equation for the zeroth wavefunction of a harmonic oscillator. I have pretty much got it but my solution just differs by a constant,so I thought why think when one can ask other people :). Here is the equation: Where the x star represent a...

Say I have a wavefunction that's a superposition of two-particle states: \Psi = \int dk ~f(k) c^{\dagger}_k c^{\dagger}_{-k} | 0 \rangle Here, ##|0\rangle## is the vacuum and ##c^{\dagger}_k c^{\dagger}_{-k} | 0 \rangle## represents a pair of fermions with momenta ##k,-k##. My goal is to solve...

Homework Statement A particle is described by the wavefunction: \psi (x) = \{ \begin{array}{*{20}{c}} {A\cos (\frac{{2\pi x}}{L}){\quad\rm{for }} - \frac{L}{4} \le x \le \frac{L}{4}}\\ {0{\quad\rm{otherwise }}} \end{array} (a) Determine the normalization constant A (b) What is the probability...

Homework Statement The wavefunction ψ(x,t) obeys the time-dependent Schrodinger equation for a free particle of mass m moving in one dimension. Show that a second wavefunction φ(x,t) = ei(ax-bt)ψ(x-vt , t) obeys the same time dependent schrodinger equation, provided a = ħa2/2m and v = ħa/m...

Homework Statement I'm asked to calculate the reflected and transmitted part of the wavefunction, in fact, this is the first time i encounter this so i need your assistance. Homework Equations Time independant schrodinger equation + continuity condition The Attempt at a Solution See the...

Homework Statement [PLAIN]http:// Question D. Homework Equations The Attempt at a Solution The wavefunction is all real. So I can simply sqaure it... However when I do this and differentiate it using the product rule, I'm getting r = 2a(naught) as the maximum and not 4a(naught)... Any...

For a particle in a stadium billiard, it is observed that so-called 'scars' in the wavefunction appear at particular eigenvectors. These scars correspond to classical orbits, for example in the case shown below, which corresponds to a classical orbit of period 6 The paths which can be...

I'm having a hard time understanding why it makes sense to say that the particle has an uncertain position to which it can collapse, but not to say that the particle has an uncertain time to which it can collapse. Similarly, why do we consider when the particle collapses as when we measure it...

Homework Statement Calculate the normalization parameter A in the wavefunction ## \varPsi(x,t) = A e^{i(k\chi - \omega t)} ## for a beam of free protons traveling in the +x direction with kinetic energy 5 keV and a density of ##7.5 * 10^9 ## particles per meter beam length. Homework...

Homework Statement Show that a real valued wavefunction ##\psi(x)## must have ##\langle \hat{p}\rangle = 0##: Show that if we modify such a wavefunction by multiplying it by a position dependent phase ##e^{iax}## then ##\langle \hat{p}\rangle = a## Homework Equations ##\hat{p} = -i \hbar...

Homework Statement A particle of mass m is confined to a space 0<x<a in one dimension by infinitely high walls at x=0 and x=a. At t=0, the particle is initially in the left half of the well with a wavefunction given by, $$\Psi(x,0)=\sqrt{\dfrac{2}{a}}$$ for 0<x<a/2 and, $$\Psi(x,0)=0$$ for a/2...

Hi. I would like to know which variables in the wave function are constant (in this local context) and which are not. The wave number for instance varies in the article I was reading (WKB approximation). Why is this so? What other variable in the wavefunction can vary? Please help me as I am...

When normalizing a Wavefunction for a particle on a ring why is the normalization only done as dPhi? It's a particle on a ring, so shouldn't it be r*dPhi? This is my thinking, but I do not find other solutions doing this, just ignoring the r part. I understand that for a ring it's just a...

So I understand that as the number of entangled particles increases, observable quantum mechanical properties decrease to the extent that the mass of particles collectively loses its wave-particle character and behaves classically. In other words, the particles' collective position-space...

How is the wavefunction of one particle with mass, m, and velocity v affected by a nearby particle that has it's own wavefunction with mass, M and velocity V. Can the interaction of these wavefunctions be through any other means than entanglement? Can the wavefunction of a single non-entangled...

Dear Physics Forum, Is the Uncertainty Principle the cause of the infinite solutions to Schrodinger's equation? I get the sense it is not. Could you elaborate a little? Thanks, Mark

Homework Statement 2. Homework Equations [/B] Uploaded as a picture as it's pretty hard to type out The Attempt at a Solution So to normalise a wavefunction it has to equal 1 when squared. A is the normalisation factor so we have: A.x2e-x/2a0.x2e-x/2a0 = 1 ∫ψ*ψdx = A2∫x4e-axdx = 1 Then I've...

Going back to the basics, I recall the wave function of quantum mechanics being dependent on space and time coordinates, such as \Psi (\overline{x},t), however one says that quantum mechanics is a 0+1 dimensional (0 space, 1 time) QFT. So there is NO SPACE. Now, I know there's the caveat that...

... and its classical wave equation? Suppose in our double sit experimental setup with the usual notion of d,D we have a light of known frequency (v) and wavelength (L)- so its y=Asin(kx-wt). It passes through the two hole and move ahead doing the usual interference stuff, so final wave equation...

I am trying to solve for the energy of 2 non-interacting identical particles in a 1D infinite potential well. I want to do it as much "from scratch" as possible, making sure I fully understand every step. H = -ħ2/2m * (∂2/∂x12 + ∂2/∂x22) Hψ=Eψ ∂2ψ/∂x12 + ∂2ψ/∂x22 = kψ, where k=-2mE/ħ2 I got...

In 4-D Hilbert space for 2 electrons is |up1>|down2> equivalent to |down1>|up2> due to electrons being identical ?

This just in: http://www.nature.com/nphys/journal/vaop/ncurrent/full/nphys3233.html

Is the collapse of the wave function of the electron in the double slit experiment based purely on the act of observation? Or could it be that the way the instrument used to measure the electron caused it to collapse by how it physically interacted with the electron? Keep in mind the delayed...

1. In griffiths the following is written down in the chapter of identical particles: ##\Psi(\vec{r_{1}},\vec{r_{2}})=\pm \Psi(\vec{r_{2}},\vec{r_{2}})## Where it's + for bosons and - for fermions. However in class we have seen that for two electrons in the spin singlet situation the POSITION...

Title basically says it all. I'm a physics undergrad trying to wrap my head around quantum physics, and I was hoping people here could help. My question comes from something in one of my textbooks. It tries to explain particle-wave duality through a piece of string, which I'll quickly go over as...

In my physical chemistry course, we are learning about the Schrödinger Equation and were introduced to the Hamiltonian Operator recently. We started out with the simple scenario of a particle in 1D space. Our professor's slide showed the following "derivation" to arrive at the expression for the...

p. 12 Introduction to Quantum Mechanics by Griffiths Equation 1.25: the differential operatot was factored. This to me seems like a mathematical trick or due to amazing foresight, but is there any underlying/guiding theory for this factorisation? Equation 1.27: the wavefunction was assumed to be...

Homework Statement (a) Find the spatial wavefunction (b)Show anti-symmetric wavefunctions have larger mean spacing (c) Discuss the importance of this (d)Determine the total orbital angular momentum (e)Hence find the ground state term for Z=15[/B] Homework EquationsThe Attempt at a Solution...

Homework Statement I'm going to list two questions as they offer the same problem with more choices, hopefully it will help realize the method (?) used (A) An electron, confined in the two dimensional region 0<x<L and 0<y<L with infinite potential walls, is subject to the potential...

when considering the quantum harmonic oscillator, you get that the wave function takes the form psi=ae^{-\frac{m\omega}{2\hbar}x^2} I have been trying to integrate \psi ^2 to find the constant a so that the wave function is normalised, and I know the trick with converting to polar coordinates...

Homework Statement After a calculation of the lowest energy using two variational parameters a and b it is found that: E_{T}(a,b) = 2a^{2} + 16b^{2}+a What is the optimal (minimum) value of E_{T} Homework Equations It's just derivation. The Attempt at a Solution \frac{\delta E_{T}}{\delta a}...

[Note from mentor: this thread originated in a non-homework forum, therefore it doesn't use the standard homework template] ------------------------------------------ This exercise pops up in the Cavendish Quantum Mechanics Primer (M. Warner and A. Cheung) but I can't seem to figure it out. So...

In first order correction of wavefunction, |ψ(1)n>=∑ψ(0)m<ψ(0)m|V|ψ(0)n>/(E(0)n−E(0)m) when any two of the original states degenerate, we replace the two states with their corresponding "good states" to get a new set of "undisturbed" states (ψ(0)m), AND then we determine the first order...

For a particle, given the normalised eigenfunctions of the Hamiltonian, the associated energy eigenfunctions and the wavefunction describing the state of the particle at time t=0 how does one calculate the wavefunction for arbitrary t? I know you could solve the time dependent Schroedinger...

Homework Statement The ground state wavefuntion of a system in spherical polar coordinates is given by: Ψ (r,θ, φ)= (A/r) [exp (-ar) - exp (-br)] where a, b, A are constants. i) Determine A as a function of a and b, so as to normalize the wavefuntion. ii) From Schrödinger equation find V (r)...

Can someone please describe the diffraction orders on a nano-grating? I am reading articles about imaging devices, and I cannot understand the diffraction orders For example, incident wave can be mapped into a propagating wave through the -1, 0, and+1 diffraction orders. Is any of these...