Wavefunction Definition and 585 Threads

Homework Statement Consider the nonstationary state: \Psi = \sqrt{\frac{1}{3}}\Psi_{22-1} + \sqrt{\frac{2}{3}}\Psi_{110} Where \Psi_{22-1} and \Psi_{110} are normalized, orthogonal and stationary states of some radial potential. Is \Psi properly normalized? Calculate the expectation value of...

Homework Statement Consider any ket. Find the perturbative correction to that ket. Then, |n> = |n0> + |n1> Here, |n0> is the ket from the unperturbed hamiltonian (who cares what it is), and |n1> is the 1st order correction. Do you introduce a new normalization when you add the...

I see why having mutiple points of infinity in the wavefunction would be bad. But what about one point being infinity and everywhere else being zero? Is this the only case where the wavefunction could have an infinite value? Would this be a case where the expectation value of whatever...

Homework Statement Ignoring the repulsion force between two electrons, one of the electrons is in 1s state and the other is in 2p state. what is the total wavefunction of the system that is made up of the multiplication of the spatial wavefunctions and spin values? Homework Equations...

In his textbook, Griffiths claims that solutions to the TISE for even potentials for a given energy can always be written as a linear combination of even and odd functions. That I understand. However, I do not see why that fact justifies only looking for even or odd solutions, as he does later...

Homework Statement The wavefunction describing state of a system is, \psi (r,\theta ,\phi )=\frac{1}{8\sqrt{\pi }}\left( \frac{1}{a_{0}}% \right) ^{3/2}\frac{r}{a_{0}}e^{-4/2a_{0}}\sin \theta e^{-i\phi } Find the parity of system in this state. The Attempt at a Solution \psi...

In a single photon at a time double slit experiment. Is it the wave function or electromagnetic wave of a photon that is interfering? If both, what is the contribution of each? Remember that the electromagnetic wave is not the wave function of the photon. In a single photon, it has wave...

Hello, I was wondering what exactly happens when you observe part of the wavefunction of a particle, does this always cause collapse? Or only when the probability distribution decides that the particle is indeed there? What I mean is, is an observation in the form of photons interacting with...

Hello, This question is related to wavefunctions and their radial and angular parts. I know how to draw the radial part, the RDF but how would you draw the angular part? Thank you!

Homework Statement This is a multi-choice question. A particle of unit mass moving in an infinite square well, V = 0 for lxl ≤ a V = ∞ for lxl > a is described by the wavefunction, u(x) = A sin (3∏x/a) If the wavefunction is normalised, What is A? a) 1/2a b) 1/√2a c) 1/√a...

Homework Statement At time t=0 free particle is found in state psi=const*sin(3x)*exp[i(5y+z)]. What values for energy and for momentum we can get if we measure them at t=0 and with what probability? Homework Equations Well, we know that eigenvalues of energy and momentum operator for...

I've been going through Sidney Coleman's QFT video lectures (http://www.physics.harvard.edu/about/Phys253.html, with notes at http://arxiv.org/PS_cache/arxiv/pdf/1110/1110.5013v1.pdf). I'm up to the part on fixing counterterms for wavefunction renormalization (page 179 in the notes), and have...

Alright, so here's my problem. I've got a wavefunction between -L/2 and L/2 (symmetric around 0). It's a square wave and it is in an infinite potential well. That's all I know about it. I need to find the wavefunction of it. I was thinking of doing a Fourier sine/cosine series but I'm stuck...

Hi all, I must misunderstood somewhere, couldn't figure out the following, any helps will be greatly appreciated. The first order correction of the pertubated energy is: \leftψn0\langle H'\rightψn0\rangle Where: ψn0 Is the solution of the unpertubated Hamiltonian. My question is can ψn0 be...

Homework Statement A harmonic oscillator is initially in the state \psi (x,0)=Ae^{-\frac{\alpha ^2 x^2}{2}} \alpha x (2\alpha x +i). Where \alpha ^2 =\frac{m \omega}{\hbar}. 1)Find the wavefunction for all t>0. 2)Calculate the probability to measure the values \frac{5\hbar \omega }{2} and...

Homework Statement For the infinite square well, a particle is in a state given by \psi = \frac{1}{\sqrt 2}(\psi_1 + \psi_3) , where \psi_1 and \psi_3 are energy eigenstates (ground state and the second excited state, respectively). Represent this state as a column matrix \psi> in...

Hi! I would like to ask everyone's opinion about this wavefunction in the momentum representation: ψ(p) = N[θ(-p)exp(ap/hbar) + θ(p)exp(-ap/hbar)], where N is a normalization constant, a > 0, and θ(p) is a function defined as θ(p) = 0 for p > 0 and also θ(p) = 0 for p < 0. I think the...

Wavefunction "collaps" past/future effect A newb writes, Do wavefunctions really "collapse?" It seems like this implies that they are destroyed and then recreated. Would it be more accurate to consider them like a guitar string and that observing it is like hitting the harmonic? I guess...

Simple question. So the energy of a particle is observed to be E_1 (for example) at time t=0. At time t=0 the wavefunction psi(x) collapses to phi(x)exp(-i(E_1)t/h). At time t>0 the wavefunction is also in this state (right?). Is it in this state until it interacts with another particle or...

Homework Statement A wavefunction in an infinite square well in the region -L/4≤x≤3L/4 is given by ψ= Asin[(πx/L)+δ] where δ is a constant Find a suitable value for δ (using the boundary conditions on ψ) Homework Equations The Attempt at a Solution Asin[(πx/L)+δ]=?

Hello, I'm trying to find out the normalization constant in a given wavefunction but I cannot. I think that this is a math problem because I cannot solve the integral of the probability density but your experience could help; I was trying several steps and I tried in the software "derive" but...

Homework Statement Normalise ψ=Ae^(-λχ)e^(-iδt) Homework Equations I know you have to intergrate ψ^2 i.e (ψxψ*) The Attempt at a Solution Im literally just stuck at the first bit , i can do the rest. I have the solutions manual and I don't understand how they get 2|A|^2 e^(-2λχ) from...

Homework Statement Consider the wavefunction \Psi (x,t)=c_1 \psi _1 (x)e^{-\frac{iE_1t}{\hbar}}+c_2 \psi _2 (x)e^{-\frac{iE_2t}{\hbar}} where \psi _1 (x) and \psi _2 (x) are normalized and orthogonal. Knowing \Psi (x,0), find the values of c_1 and c_2. Homework Equations C^2 \int...

Homework Statement Wavefunction is of form: ψ(x) = eikx Find momentum and energy of this state. Homework Equations Fourier transform of ψ(x) to get to momentum space or is it <p> = integral from -infinity to infinity of ψ* (h/i) * derivative wrt x of ψ dx The Attempt at a Solution...

Homework Statement Homework Equations The Attempt at a Solution The issue I'm having here is that the problem should be able to be done rather quickly. I can see how to solve for <H> using the operator, but there's a quick way that I'm not picking up on. I thought about solving <H> = <p^2> /...

Homework Statement An electron in a hydrogen atom is described by the wavefunction: psi(r) is proportional to (psi(subscript 100)+2psi(subscript 210)-3psi(subscript 32 -1) -4psi(subscript411)) where psi(nlm(subscript l)) are the eigenfunctions of the hydrogen atom with n, l...

Hello, I have a slight problem with Quantumtheory here. Homework Statement I have solved the schrödinger equation in the momentum space for a delta potential and also transferred it into real space. So now I have to find the correlation between the width of the wavefunction in both spaces...

The wavefunction of hydrogen is given by \psi_{nlm}(r, \theta, \phi) = R_{nl}(r)Y_{lm}(\theta, \phi) If I am only given the radial part, and asked to find the expectation value of the radial part I integrate the square of the wavefunction multiplied by r cubed allowing r to range from 0 to...

What is the experimental evidence that a wavefunction will collapse to a dirac delta function, and not something more 'smeared' out?

Homework Statement how to set up integrals for normalization of sin(\theta)e^(-i\phi) Homework Equations The Attempt at a Solution

Under what special conditions can a wavefunction that depends on a series of coordinates be written as a product of wavefunctions that only depend on one coordinate each? What can you say about the energy in this case? (This is a study/end of the chapter question (P.Chem))... I'm thinking it's...

Hi, If we have a non degenerate solution to a Hamiltonian and we perturb it with a perturbation V, we get the new solution by |\psi_{n}^{(1)}> = \sum \frac{<\psi_{m}^{(0)}|V|\psi_{n}^{(0)}>}{E_n^{(0)} - E_m^{(0)}}\psi_m^{(0)} where we sum over all m such that m\neq n. When we do the same...

If you were to measure an electron's spin, for example, will the wavefunction associated with its position also collapse?

I've always been confused about something -- I'd love for someone to clear up my ignorance. I understand that the position of a particle can be modeled as a wavefunction (a probability distribution, to my understanding) where we can describe the position as fundamentally random, but it takes on...

It's now years since I studied this, if anyone could help me remember. If I look at a hydrogen atom and it's shells. In the ground state there's 1s, the wave function is then: \Psi_{nlm}(r,\theta,\phi) = Y_{lm}(\theta,\phi)R_{nl}(r) = Y_{00}R_{10} Y_{00} = \frac{1}{\sqrt{4\pi}} R_{10}...

Homework Statement The Schrodinger equation (in atomic units) of an electron moving in one dimension under the influence of the potential -delta(x) [dirac delta function] is: (-1/2.d2/dx2-delta(x)).psi=E.psi use the variation method with the trial function psi'=Ne-a.x2 to show that...

I took QM last year and I was reading an article by T.W. Marshall entitled Random Electrodynamics in which he describes ensembles of uncharged particles which satisfy the Liouville equation. Anyway, he introduces a wave function given by \psi (x,0)=...

Hi, In Griffiths' Introduction to Quantum Mechanics, he proves an important result in the first chapter: If we normalize a wavefunction at t=0, it stays normalized at all later times. To do this, he considers the relation \frac{d}{dt}\int|\psi(x,t)|^{2}dx=...

Hello, I am a beginner on the sbject so please correct if I'm using some sloppy terminology. I'll try to be clear. Consider a Hamiltonian with degenerate energy eigenstates (say the degeneracy is on angular momentum as in hydrogen atom). Which of the degenerate eigenstates would the wave...

Hi! I have calculated various eigenstate wavefunctions for a one-dimensional system of a particle in a potential. The potential is an even function. All the wavefunctions have become either even or odd functions which I understand why. The ground-state wavefunction has always been even, is...

Homework Statement Give a physical explanation of why a spherically symmetric Ylm cannot describe the state of a system with non-zero angular momentum. Homework Equations The Attempt at a Solution I was thinking that if Ylm is spherically symmetric then the particle is equally...

Homework Statement State three conditions that must be satisfied by the wave-function of a particle that is in a bound state of a potential well. Homework Equations The Attempt at a Solution Not sure what the three are!? I can only think of one: the wavefunction must be...

What condition must a 1D wavefuntion satisfy to be normalised? Is the fact that it the wavefuntion squared has to equal the probability of finding a particle or that the wavefuntion has to be finite or something totally different?? please help, thanks

Can someone please explain why the representation of a wavefunction as an expansion of basis eigenfunctions actually gives us something of physical meaning? For example, it can tell us the probabilities of measuring a particular eigenvalue (depending on the expansion coefficients)... I mean its...

Would it be fair to say that before an observation, a wave-particle is in a superposition of many possible states but that after the observation, the wave-particle is found only in one state? Would that be analogous to saying that it goes from behaving in a very wave-like manner to behaving...

I saw in a QM mechanics book the following wave function: psi(x) = A*[1 - e^(ikx)] what is the complex conjugate of this wave function? isnt it just psi*(x) = A*[1 - e^(-ikx)] but when you multiply psi(x) by psi*(x) shouldn't you get a real value? How come I don't?

Homework Statement psi(x) = A(1 - e^(ikx)) if 0 < x < 2pi/k Homework Equations integral of psi * psi conjugate over all space = 1 The Attempt at a Solution the conjugate is psi*(x) = A(1 - e^(-ikx)) so when I multiply psi and psi* , I get 2 - e^(-ikx) - e^(ikx) I can't...

Homework Statement We were given the wavefunction for a hydrogen atom (ignoring spin) as shown in the link below We are asked to find the probability of obtaining E=E1, L^2=2 hbar^2 and Lz=hbar Homework Equations...

I was just daydreaming for a few minutes about the energy eigenvalue equation H\Psi = E\Psi. Say H described a particle in zero potential, so that all its energy was kinetic, ie. H = 0.5mv^2 = \frac{p^2}{2m} = \frac{-\hbar^2}{2m}\frac{d^2}{dx^2}. Looking at the units of \hbar these are Js, so...

How can I define what is the wavefunction if I'm given eigenvectors V1, V2,...Vn and energies E1, E2,. ..En. I know that it must be a linear combination but how about constants?