Wavefunction Definition and 585 Threads

Uncollapse of a partial-collapsed quantum state has been accomplished in the laboratory. Here is a popular article http://www.scienceagogo.com/news/20080706233709data_trunc_sys.shtml An article on this by Nadav Katz et al has just appeared in Nature News. I believe this is the preprint of...

Why shud one take the Fourier transform of a wavefunction and multiply the result with its conjugate to get the probability? Why can't it be Fourier transform of the probability directly? thank you

Hi everyone, This might belong in the quantum mechanics section, so I apologize if I placed this thread in the wrong place. My question is: how do I calculate the gradient of a multiparticle wavefunction? For example, suppose that a wavefunction \psi describing the probability...

Problem A free particle of mass m moving in one dimension is known to be in the initial state \psi(x, 0) = \sin(k_0 x) a) What is \psi(x, t)? b) What value of p will measurement yield at the time t, and with what probabilities will these values occur? c) Suppose that p is measured at...

Problem Describe the evolution in time of \phi_1 = A \sin \omega t \cos k(x+ct). Attempt at Solution We have that \partial^2 \phi_1 / \partial x^2 = -Ak^2 \sin \omega t \cos k(x+ct) \partial \phi_1 / \partial t = A \sin \omega t (-kc \cdot \sin k(x+ct)) + A \omega \cos \omega t \cos...

Wavefunction collapse ==> increase in entropy?? I just read an article in Scientific American by Sean Carroll, called something like Does Time Run Backward in Other Universes. In it, he says that the reason wavefunctions only collapse and never un-collapse is because collapsing represents an...

If in the case of two non-interacting particles, the wavefunction looks like (for bosons): \psi(x_1, x_2) = \frac{1}{\sqrt{2}}[\phi_a(x_1)\phi_b(x_2) + \phi_a(x_2)\phi_b(x_1) And to normalise the wavefunction, the modulus squared has to be found. I can do this when I can substitute...

Homework Statement If \Psi = f(x, y) and x = g(t), y = h(t), then (d\Psi / dt) = (p\Psi / px)(dx / dt) + (p\Psi / py)(dy / dt), where "p" symbolizes the partial derivative here and throughout the rest of this posting. Derive the phase velocity equation +/- v = -(p\Psi / pt) / (p\Psi / px)...

I'm not sure the double-slit experiment is one such example, maybe I have not understood it yet. This experiment shows the wave nature of light due to the wavefunctions of photons. But how does it show a particle of zero size that is not just a burst of waves?

Hi, I'm teaching myself quantum mechanics (so this isn't homework). I came across the following question: \Phi(p) = A\Theta\left[\frac{\hbar}{d}-|p-p_{0}|\right] I have to find the constant of normalization, \psi(x), and the coordinate space wave function \psi(x,t) in the limit...

[SOLVED] Perturbed Ground State Wavefunction with Parity Homework Statement A particle is in a Coulomb potential H_{0}=\frac{|p|^{2}}{2m} - \frac{e^{2}}{|r|} When a perturbation V (which does not involve spin) is added, the ground state of H_{0} + V may be written |\Psi_{0}\rangle =...

Could anyone please help with the following, rather unusual, query? I know that for spin 0 bosons, the Klein Gordon equation gives solutions that are similar to the solutions of the Schrodinger equation for a non-relativistic free particle, the only difference being that the energy used when...

I have read it said a few times that a photon cannot be described by a wave-function but I am not far enough along in my QFT to know why. What's the story here? And is this the same thing as saying that one cannot answer the question "What is the probability of observing the photon in volume...

Homework Statement Find the most likely position of the particle. Homework Equations \Psi = A[(x+1)^{2} - 1)] between x = 0 and x = 1 \Psi = 0 anywhere else The Attempt at a Solution I found A to equal \sqrt{15 / 38}... but I am not sure how to do the rest of it

Homework Statement At time t=0 hydrogen atom is in state \psi(r,0)=\frac{4}{(2a)^{3/2}}[e^{-r/a}+iA\frac{r}{a}e^{-r/2a}(-iY^{1}_{1}+Y^{-1}_{1}+\sqrt{7}Y^{0}_{1})] a) Is it possible to normalize wave function ? b) Find \psi(r,t) if at time t=0 measuring L_{z} we find \hbar Homework...

Can anyone help me understand what is meant by the "parity of a wavefunction"? I know in terms of even/odd parity, that: P \Psi(x,y,z) = \pm \Psi(x,y,z) ie, P = +/- 1 But I don't know what "parity of a wavefunction" physically means...

Homework Statement I'm trying to determine a normalization value, A, for the following wavefunction: \Psi = Ax{^2}exp(-\alpha x)}, x>0 \Psi = 0, x<0 In the past, I've had an i term in my exponential, so when applying the Normalization Condition: \int|\Psi(x)|^2 dx = \int\Psi{^*}(x)...

Hi there, i have been studying a bit about QM, but ther's one fundamental question about the wavefunction i can't understand: why is the wavef. defined complex? I mean, couldn't one work from the beginning with a real wave? Thanks

[SOLVED] hydrogen atom Homework Statement My book says that R_{1,0}(r) = 2(1/a_0)^{3/2} e^{-r/a_0} is a normalized wavefunction. But if you integrate R_{1,0}(r)^2 over r from 0 to infinity, you do not get 1. What's wrong here?Homework Equations The Attempt at a Solution

I faced a weird question:what is the requirement of having a wave equation for the QM systems? I think unless we have it,we cannot predict the probabilistic time and space evolution of the wave function subjected to potential constraints.(dynamicity of the wave function will be lost)...

Homework Statement If given, for instance, psi(phi, 0)=[1/sqrt(2pi)](cos^2(phi/2) + isin(phi)), which is the wavefunction at t=0, how do you go about finding the wavefunction at time t, psi(phi,t)?? Homework Equations The Attempt at a Solution Would it simply be psi(phi...

I am just beginning to understand this concept. Some help would be appreciated. Let me know if I am wrong in saying the following: "The wave function (say \Psi] collapses to an eigen vector of the operator corresponding to the physical quantity(say \lambda) being measured. This is because the...

Can the wavefunction collapse not be derived or is it really an axiom? How can the answer to this question (yes or no) be proven? If it is an axiom, is it the best formulation, is it not a dangerous wording? Let's enjoy this endless discussion !

I won't debate on the "wavefunction collapse" ... ... since this is just a lazy debate started from a misunderstanding. Clearly when a small system interacts with a measuring device, the wave function of the small system just loses any meaning. There is only one "larger" wavefunction for...

some very beautiful experimental work, observing the progressive collapse of a a wavefunction. beautiful illustrations too I didn't see this discussed here so decided to start a thread on it Here's the abstract http://arxiv.org/abs/0707.3880 Progressive field-state collapse and...

some very beautiful experimental work, observing the progressive collapse of a a wavefunction. beautiful illustrations too I didn't see this discussed here so decided to start a thread on it http://arxiv.org/abs/0707.3880

Near "Normalization" calculation for given wavefunction Homework Statement A wave function is given by Y(E) = CEexp(-E/kt) 1. Find C so that Y(E) becomes Y0 where Y0 is a constant. 2. Calculate the mean energy with respect to Y(E). 3. Find Y(t) as a function of wavelength and...

hey guys, this is a silly question, I'm sure it's been answered in other threads many times before and for that I am sorry. when we take a measurement on an electron (lets say position or velocity), do we change it's wavefunction? What I mean is, we have a wavefunction in time and space...

I have an infinite well from -a to with a particle in its ground. The initial wavefunction is then \psi(x) = u_1^+(x;a) = cos(\pi x/ 2a)/\sqrt{a} for |x| < a. In order to get the wavefunction for this particle when box that is instantaneously expanded to [-b,b] should I apply Fourier...

Hi all I know I raised a similar question in the thread "Wave particle duality", but it is already so full of many other questions, that I'd not be able to discuss this topic fully there. So, in the double slit experiment, if a photon observes an electron, the interference pattern...

"Inside the Wavefunction" Hi, I was thinking about the wavefunction when I intercepted an interesting thought experiment that I couldn't quite formulate the answer to: Say that we imagine a small particle that is small enough so that it is about the size of an electron (the particle...

It seems likely- but is it true that the ground state many-body wf must have zero nodes? Is there a general rule for the nodes as a fn of quantum numbers?

hey all! does anyone know the conditions a well behaved wavefunction (phi) must satisfy for all x? and any physical justifications for them? is it something to do with continuity at boundaries? or to do with the differential of the wavefunction? cheers for any input roc

Will the wave function of a particle be the same in the two cases: 1) When the particle is isolated i.e. as a free or independent particle. 2) When the particle is bonded with other similar particles to constitute a composite particle. For example, consider an isolated quark and a quark...

Homework Statement Consider the electron in an atom of the heavy isotope of hydrogen, tritium. The nucleus has charge e, and, apart from a small correction due to the reduced mass effect, the electron has energies and eigenfunctions that are identical to those of an ordinary hydrogen atom...

Homework Statement a)Write Complete wave function for an electron in a 2s orbital of hydrogen b)find the probability that the electron is at a distance from the nucleus that is outside the radius of the node. c)graph the radial distribution function for this system. Homework Equations...

When does the wavefunction propagate at a finite speed, and when instantaneously?

When you study in a book basic quantization of the string lagrangian you can see two basic ways. On ne hand you can see the X^\nu(\sigma,\tau) coordinates of the worldsheet as fields and to make canonical quantization with them. On the other hand there is teh polyakov path integral. But...

Sorry, another quick question. If I have a particle confined in a region of space -4 <= Z <=6 where psi(x)= A(4+z), -4<= z <=1 A(6-z), 1<= z <=6 0 , everywhere else And I sketch the wavefunction based on the above definitions, what is the actual equation for...

In this problem I am given a function a(k) = \frac{C \alpha}{\sqrt{ \pi}} e^{-\alpha ^2 k^2} where alpha and C are both constants Now I am supposed to construct \psi (x,t) My work: \psi (x,t) = \int_{-\inf}^{\inf} a(k) e^{i[kx - \omega (k) t]} dk pull out the constants from our...

Why does one refers to it as a "minimum uncertainty" wavefunction?

I am not a scientist - I am a retired software engineer. But I find the current interpretations in quantum physics rather unsatisfying. This leads me to some questions. My main concern is over the need for a wave function. I've recently been reading the transactional interpretation but it...

For those who have the book, this is problem 1.4 from Griffiths, 2nd ed. \psi (x,0) = \left\{ \begin{array}{rcl} A\frac{x}{a} & \mbox{for} & 0 \leq x \leq a \\ A\frac{b-x}{b-a} & \mbox{for} & a \leq x \leq b \\ 0 & otherwise \end{array}\right. a) Normalise the wavefunction. I found...

I start with calculating psi(x,0). Then i use fft(psi(x,0)) to get the Fourier coefficients. and with fftshift i get the terms with negative index in the beginning. Then i multiply with the timedependent factor and use ifftshift and ifft to get the wavefunction psi(x,t). Here is the code...

Well, the question goes like this, A particle of mass m is trapped in an infinitely deep one-dimensional potential well between x = 0 and x = a and at a time t=0,, the wave fuction is given as Φ(x,t=0)=sin(((πx)/a))cos(((2πx)/a)) (i) What possible values may be found for energy of...

OK - the question gives me two bosons with 0 spin (and the wavefunctions/energy levels) and tells me to find the total wavefunction and energy for the ground state and first excited state. Now, I know the total wavefunction must be symmetric. I know the symmetric spatial part. But the spin...

Hi all, we know that the state of material particles (like electron) can be described by a wavefunction and that the wavefunction has a probabilistic interpretation. I have studied at very introductory level the quantum theory of electromagnetic radiation and it seems that it is built up in a...

A particle has mass 'm' and potential V(x) = x^2. Find the ground state of this wavefunction. Should I use the Hamiltonian operator here?

Hello, I'm writing a program, and while I have a decent understanding of wavefunctions and atomic orbitals, this one appears to be a problem I can't beat. I'm graphing various properties of atomic orbitals (wavefunction, wavefunction squared, radial probability distribution, and a cross...

I have a wavefunction given by: \psi = \sqrt{\frac{2}{L}}\sin \frac{n\pi x}{L} With boundary conditions 0<x<L. When I compute the expectation value for the momentum like this: \overline{p_x} = \int_0^L \sqrt{\frac{2}{L}}\sin \frac{n\pi x}{L} \left(-i\hbar \frac{\partial}{\partial...