Wave function Definition and 865 Threads

First of all, let me copy the standard solution from Griffiths, section 2.5, just for the sake of clarity. PotentialV(x) = - \alpha \delta (x) The bound state eigenfunction: \psi (x) = \left\{ \begin{array}{l} B{e^{\kappa x}}{\rm{ (}}x \le 0{\rm{)}} \\ B{e^{ - \kappa x}}{\rm{...

1. The wave function for a wave on a taut string is given below, where x is in meters and t is in seconds. y(x, t) = (0.300 m) sin(11πt - 3πx + π/4) (a) What is the average rate at which energy is transmitted along the string if the linear mass density is 75.0 g/m? (b) What is the...

Homework Statement The hamiltonian of a free relativistic particle moving along the x-axis is taken to be H=\sqrt{p^2c^2+m^2c^4} where p is the momentum operator. If the state of the wave function at time t=0 is described by the wave function \psi_0(x) what is the wave function at time t>0...

Homework Statement Evaluate the expectation value of p and p² using the momentum-space wave function Homework Equations Momentum-space wave function: \sqrt{\frac{d}{\hbar\sqrt{\pi}}}e^{\frac{-\left(p'-\hbar k\right)^2d^2}{2\hbar^2}} The Attempt at a Solution I can get \langle...

Hi. I'm trying to study the very basics of quantum physics and I ran into a problem. Does a free particle which is at zero potential wavefunction have some points where it's zero? So the probability of finding it would be zero? I know there is if the region has boundaries like in infinite...

I learned (University Physics, 9th Edition, Extended Version) that the wave function of a particle having a definite energy is independent of time. This means the probability Density of the particle don't change with time, i.e. If a particle is 90% likely to be found some where now, There is...

normalize the wave function and more! Please help! Homework Statement i) Normalize the wave function ii) Calculate <x> iii) Calculate <x^{2}> iv) What would happen if a < 0? Homework Equations \psi\left(x\right) = N\left(1+i\right)exp\left(-a|x|\right), for -inf <...

For an N- electron system, how to construct a wave function? One wave function for each electron or one wave function for the entire system>

The "wave nature" of the wave function. Let's say an electron has a certain wave function in two dimentions, and a proton or electron travels through it (the wavefunction). Will the wavefunction of the electron experience "wave effects" like if one drove a piece of wood through a body of...

Hi! In every qm exercise I have the wave at time t=0 and I have to study its evolution in time. But experimentally, how can I get the wave function at time t=0? For example, if I am studying the motion of my car, how can I get its wave function?

There are four commonplaces that I am not sure how to mesh together, or if this is not possible, which one(s) is/are an () oversimplification(s)/wrong, and why. (1) the wavefunction is deterministic. (2) a collapse or decoherence or splitting into worlds (take your choice) makes the wave...

Homework Statement The wave function in state n=2 is given: W2(x)=(2/L)^(1/2)sin(2pix/L) with boundaries x=0 and x=L at x=L/2, W2(L/2)=0, which means that the probability of finding the particle in a small region about x=L/2 is zero. Nevertheless, there is equal probability to find the...

Homework Statement The ground state wave function of a one-dimensional simple harmonic oscillator is \varphi_0(x) \propto e^(-x^2/x_0^2), where x_0 is a constant. Given that the wave function of this system at a fixed instant of time is \phi\phi \propto e^(-x^2/y^2) where y is another...

Homework Statement The wave function of a state is Psi(x)= N*a(x)exp(i*p0*x/h)where a(x) is a quadratically integrable real valued function Show that the expectation value of the function is p0. Homework Equations The Attempt at a Solution The only thing I'm having a problem...

Hello, As we know, the wave function of infinite potential wells form a complete orthogonal base. I have tried now to solve out the wave function for finite potential well, checking the orthogonality, I found that they are no longer orthogonal to each other (I mean the wave function...

for example, if the hamiltonian of a system is transformed this way: H(x) --> H(x+a) i understand that the tranformation can be represented by a unitary operator U=exp(iap/\hbar) UH(x)U^{*}=H(x+a) but what happens to the wave function? how is it transformed?

Homework Statement which of the wave functions describe a wave that moves in the -x direction y(x,t) =Asin(-kx-wt) y(x,t)=Asin(kx+wt) y(x,t)=Acos(kx+wt) Homework Equations wave function The Attempt at a Solution I know B and C both move left looking at the phase (kx+wt) because...

Sorry people but some quantum mysteries look quite trivial to me. Wave function collapse for photons is actually subsampling of whole sample of photons. That way wave function collapse can happen instantaneously in the whole experimental setup or even backwards in time. Photon entanglement...

Homework Statement Mean value and deviation of momentum for this wave function: \Psi(x,0)=cos^2(kx/L)e^{2ikx/L} Homework Equations The Attempt at a Solution I express the cos^2 in terms of exponencials: \Psi(x,0)=(1/2)+(1/4)e^{2ikx/L}+(1/4)e^{4ikx/L} the momentum of...

What about the act of observation actually causes a particle to break the superpostion and "decide" what its state is? What property does the observer posses that changes the the way particles behaves?

I am imagining the collision between two subatomic particles. For the particles to have collided, do we say that the spatial wave functions for each particle must have collapsed to the same point? Or do we say that the particles are just in a very close vicinity, and the wave functions need not...

Homework Statement I am unfamiliar with LaTeX (is there a tutorial around, or should I just wing it and risk posting a potential mess?). my problem is that I need to normalize a wave function: psi(x,t) = Ae^(-bx)e^(-iwt). there are no constraints given. Homework Equations integral of...

Homework Statement im quite confused of describing whether these wave functions y(x,t)= sin(kx-wt) ; y(x,t)=sin(kx+wt) ; y(x,t)=cos(kx-wt) ; y(x,t)=cos(kx+wt) travel to the right or to the left. My prof told me that y(x,t)=sin(wt-kx) travels to the right (+x direction) but based on my...

Homework Statement normalize the wave function \Psi(x)= Acos(\Pi*x/a) to show that A=\sqrt{2/a} The Attempt at a Solution i don't know how to get that answer as all i can tell, normalizing gives: -A^{2}pi^{2}2x/a^{2} * sin (pix/a) However this does not give the right answer for A Any...

Homework Statement I'm starting to (trying) teach myself some quantum mechanics out of the Griffiths book, and since there are no answers in the back I have no idea if I'm on the right track or not. Could you guys look over the answer to this equation to see if it looks right? Consider the...

Homework Statement Show that the antisymmetry of the two nucleon wave function in an oscillator model implies that L + S + T = odd. Secondly would this condition change if one worked in a more general single particle model? T = isospin S = intrinsic spin L = orbital angular momentum...

Homework Statement At a given point, the wave function of a particle in a non normalisable state is 1+sin^2(kx). When you measure thekinetic energy, which values are expected and with which probabilities? Homework Equations K=<P2>/2m The Attempt at a Solution I guess I should...

The hydrogen atom 1s wave function is a maximum at r = 0. But the 1s radial probability density, peaks at r = Bohr radius and is zero at r = 0. can someone explain this paradox?

I have a question on collapsing wave functions. Suppose one observes the wave function of an electron. The wave function should collapse, but would it collapse instantaneously? If so, wouldn't this violate relativity?

Homework Statement an electron moves in 1D and is confined to the right half (x>0) potential: V(x) = -(e^2)/(8piEx) E is the permittivity of free space the ground state wave function is Nxe^(-ax) N is normalization constant, and a is another constant needed to be determined Homework...

Homework Statement Suppose a hydrogen atom is in the 2s stat, with its wav function given by: \psi_2_s (r) = \frac{1}{4\sqrt(2\pi a_o^\frac{3}{2})} (2-\frac{r}{a_o}) e^(-\frac{r}{2a_o}) Taking r = a_o, calculate \psi_2_s (a_o) Homework Equations The Attempt at a Solution...

Show that for ψ1 , ψ2 ∈ C, |ψ1 + ψ2 |^2 can take any value in [0, 4α], where α = |ψ1 |^2 = |ψ2 |^ 2 I think the solution has something to do with triangular identies but I am not sure how to start this problem at all.

http://arxiv.org/abs/0902.1464 Does wave function collapse cause gravity? Authors: Lajos Diósi (Submitted on 9 Feb 2009) Abstract: We give a twist to the assumption - discussed in various earlier works - that gravity plays a role in the collapse of the wave function. This time we discuss...

Hi all: I am confused that in general case, if [H,p]=0 (where H is Hamiltonian of system and P is parity operator), system wave function is either symmetric or antisymmetric. How do we know that system is in lower energy state if its wave function is symmetric by comparing that system is...

Homework Statement The ground state wave function for the electron in a hydrogen atom is: \psi(r) = \frac{1}{\sqrt (\pi a_o^3)} e^\frac{-r}{a_o} where r is the radial coordinate of the electron and a_o is the Bohr radius. Show that the wave function as given is normalized...

Poor title. Actually I have a whole bunch of wave function questions. I don’t know the boundaries of this concept. Assuming a correct wave function, can a particle have more than one? Can 2 observers each have their own wave function? The moment a particle encounters another particle, does one...

Hi! I would like to know if there is any direct experimental evidence of the electron distribution inside of the hydrogen atom. In the Wikipedia article http://en.wikipedia.org/wiki/Hydrogen_atom" you can see the solutions of the Schrödinger equation and the graphical representations of the...

Suppose \psi(x) is an eigenfunction of some Hamilton's operator H (H\psi)(x)=-\frac{\hbar^2}{2m}\partial_x^2\psi(x) + V(x)\psi(x). I've noticed that it seems to be true, that if the eigenvalue corresponding to this eigenfunction is isolated in the spectrum (I merely mean the set of...

Hi everyone, Assume that we have an electron in the Coulomb field of a proton, whose wave function is specified. How can I find the probability of finding this electron in the ground state of the hydrogen atom? Thank you.

Homework Statement A problem from an examination: A hydrogen atom is in the state \Psi=A(\sqrt{6}\psi_{100}+\sqrt{2}\psi_{200}+\psi_{211}+2\psi_{31-1}+\sqrt{3}\psi_{321}+3\psi_{32-2}) where \psi_{nlm} are the eigenfunctions of hydrogen. Find A so that the equation is normalized. Homework...

Hi, I have a few question about orbitals 1. What does psi or wave function represents? 2. When talking about orbitals what does phases actually mean (does it relate to charge and electron spin)? 3. What's the mechanic behind when phases cancel out to create sigma*1s antibonding...

Hi, I am new here. I am a graduate student of department of physics at some university in Korea. If there is any wrong in my english, I will apologize in advance. I am preparing for my qualifying exam that is going to be held on next month. Homework Statement The question is very simple as...

Homework Statement One wave function of H like atom is \psi=\frac{\sqrt{2}}{81\sqrt{\pi}a_{0}^{3/2}}(6-\frac{r}{a_{0}})\frac{r}{a_{0}}(e^{\frac{-r}{3a_{0}}})cos \theta How many nodal surfaces are there? 1)1 2)2 3)3 4)none of these The Attempt at a Solution Its an objective...

A wave function(psi) is a mathematical quantity which gives complete information about the state of a system at a particular instant of time. But what information does the complex conjugate of a wave function(psi*) give? Does it represent the same state as psi? Or does it just have a...

Homework Statement \psi_{n}(\theta)=A_{n} \exp(\imath n \theta) where n is an integer Calculate the factor A_{n} if the wave function is normalized between \theta = 0 and \theta = 2\pi. Homework Equations NA The Attempt at a Solution 1=\int_0^{2\pi} |\psi_{n}(\theta)|^2...

hello all

what is a wave function? And how do we define a wave function? How is it related to schrodinger's equation?

A transverse sinusoidal wave on a string has a period of 25 ms and travels in the negative x direction with a speed of 30 m/s. At t=0, a particle on the string at x=0 has a displacement of 2 cm and is traveling downward with a speed of 2 m/s. Find the amplitude, phase constant, and maximum...

Homework Statement A system's wave function has the form \psi(r, \theta, \phi) = f(t, \theta)cos\phi With what probability will measurement of L_z yield the value m = 1? Homework Equations L_z|\ell, m> = m|\ell, m> The Attempt at a Solution I feel like there may be a typo...

The Perimeter Institute has a talk on the Feynman chessboard / checkerboard model scheduled for a few days from now. This will be recorded and you can play it back, sometime after November 18th. Links: Speaker(s): Garnet Ord - Ryerson University Ord's website...