Wave function Definition and 878 Threads

Find the probability current of Ae^i(kx - ωt) + Be^-i(kx+ωt) Ok, to my understanding the probability current is the probability that you will find a certain particle as it moves with time, thus the probability of finding it changes with time. Quantum physics is a tricky one to grasp, I've...

I understand a normal mechanical wave, simply a disturbance that moves. But, I want understand a quantum wave function, mainly how you can describe a wave by the particle it self?

So, I am reading this paper on the physicality of the wave function and I have a question. Here's the passage: "If the wave function is a physical field, then the mass and charge density will be distributed in space simultaneously for a charged quantum system, and thus, there will exist...

what happens to the continuity of wave function! In the presence of a delta potential, how does the continuity of the wave function gets violated?

Homework Statement ψ(x)=A((2kx)-(kx)^2) 0≤X≤2/k ψ(x)=0 everywhere else I need to find A Homework Equations ∫|ψ(x)|^2 dx=1 so I know I need to evaluate it between 0 and 2/k The Attempt at a Solution My problem is do I square the whole ψ(x)? If some one could point me in right direction I...

Homework Statement I was reading up on the Wave Function used in the Schrodinger Wave Equation. However one source said that ψ(x,t)=e^(-i/hbar*(px-Et)) Another source had this ψ(x,t)=e^(i/hbar*(px-Et)) Which one of these is true and could someone give a derivation for the correct...

Here is a question I would like answered. The wave function I am going to use for this example is the ground state of the infinite well but I assume the outcome to this problem will apply to any wave function. Ground State: ψ = √(2/a)*sin(∏nx/a) , where 0 < x < a Lets say that I know a...

http://books.google.rs/books?id=vrcHC9XoHbsC&pg=PA200&lpg=PA200&dq=nolting+RKKY&source=bl&ots=5uSDg8czCj&sig=EQuk5fj-wEfHMKApWVVjeBs8ncQ&hl=sr&sa=X&ei=AeSHUIOoA-jm4QT5poCYBg&ved=0CB0Q6AEwAA#v=onepage&q=nolting%20RKKY&f=false Here in the page 203 is defined...

In Griffiths' page 36/37 he says "As we'll see in Chapter 3, what |Cn|^2 tells you is the probability that a measurement of the energy would yield the value En (a competent measurement will always return one of the "allowed" values - hence the name - and |Cn|^2 is the probability of getting the...

I am (attempting to) learn the *basics* of quantum physics in terms of the origin of atomic orbitals from the Schrodinger equation. I understand that the solution for H is split into a product of 2 functions, the radial wave function and the angular wave function. Then I am being shown plots...

Homework Statement An electron in a hydrogen atom is in a state described by the wave function: ψ(r,θ,φ)=R(r)[cos(θ)+eiφ(1+cos(θ))] What is the probability that measurement of L2 will give 6ℏ2 and measurement of Lz will give ℏ? Homework Equations The spherical harmonics The...

the probability of finding particle is a constant with time <ψ|\partialψ/\partial(t)> = -<\partialψ/\partial(t)|ψ> , the equation holds for all ψ so the time derivative operator is an anti-hermitian operator, but then consider any hermitian operator A, the rate of change of A is d(<ψ|Aψ>)/dt =...

Homework Statement Homework Equations The solution which I found: http://www.lamst-a.net/upfiles/mRA51397.png The Attempt at a Solution I tried to solve part (a) http://www.lamst-a.net/upfiles/wFU51621.jpg Please explain it to me.

Hi, how do you describe the wave function of fire or a flame?

So I understand why the limit of the wave function as x goes to infinity is 0. But on pg 14 of Griffiths 2nd ed. qm for example, why does he call lim x\rightarrow\infty ψ*\frac{dψ}{dx} = 0? How can you assume that \frac{dψ}{dx} doesn't blow up at x = ∞

For a two-electron atom, this book says that the overall wave function is either a) the symmetric space function times the antisymmetric spin function or b) the antisymmetric space function times the symmetric spin function. However, in another problem which involves two fermions in a harmonic...

for a square wave function, f(x)= { -1, -∞ ≤ x ≤ 0; +1, 0 ≤ x ≤ ∞ Expanding it in Fourier series gives a function like, f(x) = (4/π) * Ʃn=0∞( (sin ((2n+1)x) / (2n+) ) Plotting a graph of the equation gives something like this, http://goo.gl/vFJhL which obviously doesn't look like a...

i was going through the quantum mechanics book by griffith and on the very first chapter i read that the wavefunction of the quantum particle collapse on measurement. and if the interval between the succesive measurement is shorter the particle will be found at the very same location. the...

Is the wave function a "relative" wave (entanglement) Alice and Bob build a quantum entanglement experiment with the help of a lab technician. The experiment runs and a quantum entangled pair is created but unbeknown to Alice & Bob the technician puts his own measuring device in the...

Does anyone have a calculation that can calculate a particle wave function over 1 Planck time interval?

Do the units of a wave function vary? i have heard that it just joules. What do you think?

I have some doubts about the implications of the orbital angular operators and its eigenvectors (maybe the reason is that I have a weak knowledge on QM). If we choose the measurement of the z axis and therefore the Lz operator, the are the following spherical harmonics for l=1...

Homework Statement A one-dimensional wave function associated with a localized particle can be written as \varphi (x) = \begin{cases} 1- \frac{x^2}{8}, & \text{if } 0<x<4, \\ C_1 - \frac{C_2}{x^2}, & \text{if} \,x \geq 4. \end{cases} Determine C_1 and C_2 for which this wave...

HI,everyone.I have a problem. the angular portion of wavefunction of hydrogen,like 3d. n=3,l=2,so m=2,1,0,-1,-2.I read some books that say dxy,dxz,dyz,dz2,dx2-y2,so what the corresponding Relation between them. for example,dz2 corresponding what ?m=0?? and why? any help will be highly appreciated!

Hi all, I'm doing a practice question in which we have a hydrogen atom in the state: \psi = (2\psi_{100} + \psi_{210} + \sqrt{2}\psi_{211} + \sqrt{3}\psi_{21 -1})/\sqrt{10} It says that, now a measurement is taken and we find the angular momentum variables to be L = 1 and L_z = 1. The...

Homework Statement The book defines a 1/2 wave odd symmetrical function as each 1/2 cycle is a mirror image of the next. \begin{array}{l} {a_0} = 0 \\ {a_n} = {\textstyle{4 \over T}}\int_0^{{\raise0.5ex\hbox{$\scriptstyle T$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle...

Why do we consider evolution of a wave function and why is the evolution parameter taken as time, in QM. Look at a simple wave function $\psi(x,t) = e^{kx - \omega t}$. $x$ is a point in configuration space and $t$ is the evolution parameter. They both look the same in the equation, then why...

I'm curious as to whether or not there is a connection to be drawn between the phenomenon of wave function collapse and the idea of Bayesian inference. I began thinking about this within the context of one of the variants of the Monty Hall problem. If you have one kid, what's the probability...

Is the wave function, an unreal (but a useful mathematical) tool, to partially model a real interaction? i.e. can probabilities have an existence of their own? i.e. exist by themselves without referring to some underlying phenomena? The wave function is a mathematical/probability tool. It is...

I don't know if I got this right, but as far as I know, if you are able to deduce through which slit the particle went through, it behaves classically, if you have no way of deducing through which slit the particle went through, it behaves in a quantum way (interference pattern). Now, I don't...

when a wave-function splits into two paths (such as in a double slit or a mach-zehnder) how does the Schrodinger equation deal with it? when one of the path is blocked (before/after the slits or anytime prior to reaching the detector) by an opaque obstruction, how is the energy for the...

Homework Statement Consider the semi-infinite square well given by V(x) = -V0 < 0 for 0≤ x ≤ a and V(x) = 0 for x > a. There is an infinite barrier at x = 0 (hence the name "semi-infinite"). A particle with mass m is in a bound state in this potential with energy E ≤ 0. Solve the Schrodinger...

Hi, I've been reading a QM book and it mentions that particles can be represented as a wave packet, which provides a description for particles simultaneously as a wave and particle. It also mentions that the wave packets disperse, and the width becomes extremely large for free microscopic...

What is the difference between eigenfunction and wave function? I'm always get confused when i am asked to write wave function and eigenfunction..

Homework Statement "The angular part of the wave function for the dxy orbital is (√(15/∏)/4)sin^2(θ)sin(2ϕ). Show that this expression corresponds to the dxy orbital" Homework Equations conversion of Cartesian to spherical coordinates: r=√(x^2+y^2+z^2) cosθ=z/r tan(ϕ)=y/x trig...

Homework Statement "The angular part of the wave function for the dxy orbital is (√(15/∏)/4)sin^2(θ)sin(2\phi). Show that this expression corresponds to the dxy orbital" Homework Equations conversion of Cartesian to spherical coordinates: r=√(x^2+y^2+z^2) cosθ=z/r tan(\phi)=y/x...

1. Find \ C \ in \ terms \ of \ x_0 \ such \ that \ \psi(x,0) \ is \ normalized, \ where \ C \ and \ x_0 \ are \ constants. 2. \psi(x,0)=Cexp\left (-\frac{\left |x \right |}{x_0} \right ) 3. \\ \psi(x,0)=Cexp\left (-\frac{\left |x \right |}{x_0} \right )\\ \Rightarrow \psi(x,0)=Cexp\left...

Hi :), recently I was thinking whether every bound state is only real or imaginary, not mixture? Since all bound states have degeneracy of level one, if we suppose that ψ=ψ_{r}+iψ_{i}, then ψ_{r} and ψ_{i} must be linearly dependent as in opposite case there would be a bound state with...

We have the wave equation in classical mechanics in one dimension in the following way \frac{\partial^2 \psi}{\partial x^2}=c^2\frac{\partial^2 \psi}{\partial t^2} on the other hand we have the Schrodinger equation in quantum mechanics in one dimension in the following way...

Homework Statement I've been asked to find the value of c and the probability that the electron is located in the range of x=-1 and x=1. Homework Equations See Graph below The Attempt at a Solution ψ graph http://img850.imageshack.us/img850/61/wavefunction.jpg |ψ|^{2} graph...

According to this review: http://lanl.arxiv.org/pdf/quant-ph/0508202v1.pdf A classical EM plane wavefunction is a wavefunction(in Hilbert space) of a single photon with definite momentum(c.f section 1.4) , although a naive probabilistic interpretation is not applicable. However, what I've...

For the last step in the derivation of the Gross-Pitaevskii equation, we have the following equation 0=\int \eta^*(gNh\phi+gN^2\phi^*\phi^2-N\mu\phi)\ dV+\int (N\phi^*h+gN^2(\phi^2)^*\phi-N\mu\phi^*)\eta\ dV, where \eta is an arbitrary function, g,N,\mu are constants, h is the hamiltonian for...

I have read many papers stating that the wave function of graphene has two components due to the fact that the unit cell of graphene consists of two carbon atoms (A and B atoms). However, I was confused about that. If the unit cell consist of more atoms, what will the wave function be? Does it...

I have what is probably a very basic question about the Schrödinger's cat thought experiment. As I understand it, in order for the counter tube to break and release the deadly poison, the Geiger counter must measure whether or not an atom decays. So, why doesn't that measurement collapse the...

How to prove that wave function at \Gamma point can always be a real function? I know it is not true for general k point, but for \Gamma and other high symmetry point like X, is there a simple proof? Thanks!

Homework Statement a) Find the normalization constant N for the Gaussian wave packet \psi (x) = N e^{\frac{-(x-x_{0})^{2}}{2K^{2}}}. b) Find the Fourier Transform and verify it is normalized. 2. The attempt at a solution a) I think I've got \psi (x) = N e^{\frac{-(x-x_{0})^{2}}{2K^{2}}} \int...

Homework Statement A particle may be represented in the space, -a \le x \le a, by the wave function \Psi (x) = A cos(\frac{\pi x}{2a}). Find the normalization constant Homework Equations \int |\Psi (x)|^{2}dx=1 The Attempt at a Solution In reading the question it defines the...

I have not started studying quantum mechanics in depth (so I don't know too much of the math behind it). But I read about the Schrodinger's wave equation and how it can be applied to a system when there are more than one particle (for example, hydrogen atom, a molecule etc). However, if the...

Homework Statement Suppose that at one instant in time the wavefunction of a particle is ψ(x) = \sqrt{b}e-b|x| Estimate the uncertainty of Δx for this wavefunction. Homework Equations ΔxΔp ≥ h(bar)/2 h(bar) = h/2pi The Attempt at a Solution Do I just calculate the...

Hi, why is the wavefunction not measurable as it is, but is measurable when the square of the absolute value is taken? Thank you