Wave function Definition and 865 Threads

Heads up, I only recently got into quantum mechanics and don't feel like I got a solid grasp on the material yet. 1. Homework Statement Given is the wave function of a free particle in one dimension: \begin{equation} \psi(x,0) = \left( \frac{2}{\pi a^2} \right)^{1/4} e^{i k_0 x} e^{-x^2/a^2}...

According to WKB approximation, the wave function \psi (x) \propto \frac{1}{\sqrt{p(x)}} This implies that the probability of finding a particle in between x and x+dx is inversely proportional to the momentum of the particle in the given potential. According to the book, R. Shankar, this is...

Just a reminder to you all, I am just a layman... These experiments were both done is what is called a penning trap. I think this only proves the version of MWI where the universe doesn't actually split. The "bare" theory, where no new matter is created. According to MWI an electrons...

What exactly do you mean by observing a state/ collapsing wave function. What is observing? Is it seeing the particle? Hearing? Also how cautious do you have to be near a quantum computer so that you don't collapse its wave function?

Homework Statement I post here to check if I am in the right way to understand this point in the book. The wave function of free particle is ##Ae^{\frac{i}{\hbar}(px-Et)}##.This could be regarded as ##{\phi}(x,t)=Ae^{\frac{i}{\hbar}S(x,t)}##. ##S(x,t)## is the free particle's least action...

I have to calculate the Expectation Value of an Energy Eigenstate : < En > The integral is ∫ ψ* En ψ dx I have : A ) ψ = √L/2 sin nπx/L , a single standing wave of the wave function B ) ψ = BsinBcosD , the wave function of the particle C ) ψ = ΣCn ψn = C , sum of all the...

Are two entangled photons described by the same wave function or wave function shape? Heres an example... Say for example, we have a laser in TEM01 mode that is shooting individual photons (this mode as two distinct maxima). Then the individual photons are going through a BBO crystal to become a...

Are interpretations that are non linear with respect to the wave function (eg. GRW, transactional) compatible with string theory?

Is there a psi ontic version of the Copenhagen interpretation ( where the wave function is regarded real)? Can the wave function be real in Copenhagen interpretation?

Homework Statement Prove that ##\psi_n## in Eq. 2.85 is properly normalized by substituting generating functions in place of the Hermite polynomials that appear in the normalization integral, then equating the resulting Taylor series that you obtain on the two sides of your equation. As a...

It is mentioned that subsystems don't have a wave function, in general. If two subsystems are entangled, there can be a wave function for the composite system, but not for each subsystem. Let's say you have two entangled photon pair.. it has a wave function but not for each separate photon...

What has confused me for a long time is the interaction between superposition and entanglement. That is, what happens when one member of a pair of entangled particles passes through a filter that selects for an observable that is incompatible to the observable in which the pair is entangled...

I have a concern about having some wave function psi, that is originally a superposition of many eigenstates (energies). Traditionally, it is said that the square of the coefficient of each of the component eigenfunctions represents the probability of measuring this particular energy eigenstate...

Homework Statement "assume that the three real functions ψ1,ψ2, and ψ3 are normalized and orthogonal. Normalize the following function" ψ1 - ψ21/(sqrt2) + ψ3sqrt(3)/sqrt(6)Homework Equations This is for a physical chemistry class. I haven't seen an example like this. All that is in our...

AS is a local quantum field theory, so I'm assuming that it is? What do you guys think?

Is there a relationship between the quantization of an object and its wave function? If an object isn't quantized does it have a wave function? For example, in string theory branes are not quantized, so do they have wave functions?

Do higher dimensional branes, like the super membrane (which is a 2D brane) or the NS5/M5 brane, have wave functions? I know that they become unstable once they are quantized, but does that mean that they do not have wave functions? You will never here about any thing regarding an M2 wave...

Suppose the Copenhagen interpretation is correct. And we reverse time, what happens. If a wave function has collapsed, and we found a particle somewhere. Now, I turn back time( just hypothetically), what would happen? Would the wave function uncollapse and would the particle then appear at some...

Hellow i want to ask about guessing the trial wave function at variational method of approximation usually for example at solving harmonic oscillator or hydrogen atom we have conditions for trial wave function but in fact i want to ask generally how could i make the guessing .. some problems...

Schrodinger developed his famous wave equation which describes how the quantum state of a system changes over time. But, what was Schrodinger trying to initially prove with his equation?I assume that it has to do with Debrogile's hypothesis. I know from my classes that we use the Schrodinger...

Is it possible to build the full wave function for a simple problem in QM, such as an infinite well, without any experimental data ? I'm learning about QM, and I saw how to compute energy states (the wave function for each allowed energy level) in some usual QM basic problems. But then, I was...

From the path integral approach, we know that ## \displaystyle \langle x,t|x_i,0\rangle \propto \int_{\xi(0)=x_i}^{\xi(t_f)=x} D\xi(t) \ e^{iS[\xi]}##. Now, using ## |x,t\rangle=e^{-iHt}|x,0\rangle ##, ## |y\rangle\equiv |y,0\rangle ## and ## \sum_b |\phi_b\rangle\langle \phi_b|=1 ## where ## \{...

Hi, Can anyone please explain the physical meaning of coherence(Quantum Mechanics). Thanks is advance

I need to solve Cn for a wave function, and have reached the following integral: Cn = -[√(1/a)](a/nπ)[cos(nπx/a)(ψ1(x)+ψ2(x))+∫cos(u)(dψ1(x)/dx)dx+∫cos(u)(dψ2(x)/dx)dx]This is a simplified version of the original equation, for elaboration Cn is the constant for linear combinations of a wave...

How do you find the wave function Φα when given the Hamiltonian, and the equation: aΦα(x) = αΦα(x) Where I know the operator a = 1/21/2((x/(ħ/mω)1/2) + i(p/(mħω)1/2)) And the Hamiltonian, (p2/2m) + (mω2x2)/2 And α is a complex parameter. I obviously don't want someone to do this question...

Homework Statement An interaction occurs so that an instantaneous force acts on a particle imparting a momentum ## p_{0} = \hbar k_{0}## to the ground state SHO wave function. Find the probability that the system is still in its ground state. Homework Equations ##\psi _{0} =\left(...

Homework Statement Let us look at a 3-dimensional potential box. Show, that the wave function in this situation can be written as the product of 3 single-argument functions. Homework Equations The 3D Schrödinger equation: \begin{equation} -\frac{\hbar^2}{2m} \left( \frac{\partial^2...

I have been trying to understand why two woodwind bore shapes behave so differently. My understanding is that one end of a woodwind is an antinode (driven by the reed of the instrument) and the other end is a node (where the tube is open to the atmosphere). a - - - - - - - - - - n In the...

Homework Statement I don't see how the author normalizes ##u(r)=Asin(kr)##. From Griffiths, Introduction to Quantum Mechanics, 2nd edition, page 141-142: http://imgur.com/a/bo8v6 Homework Equations ##\int_0^{\infty} \int_0^{\pi} \int_0^{2\pi}|A|^2 \sin^2(\frac{n\pi r}{a})r^2 \sin \theta...

As you can see from figure 4.4 from Griffiths book on QM, the radial wave function of the hydrogen atom has clear points where ## |R_{nl} (r)|^2 = 0 ##. My question is three fold: First, how is the electron able to traverse this region? My intuition is that with the uncertainty principle, the...

In the (b),I have some questions: (1) Does it mean ψ can be real or not real? (2) Why do the solutions of linear combination must have the same energy? As I know, these solutions are often different, as long as they are eigenvalues of time-independent Schrodinger equation. (3) In the sentence...

It seems to me that we don't measure a particle because a particle doesn't have an objective existence independent of the wave function or does it? The wave function in this case would have to be real because you can't have probability without the underlying possibility of a specific outcome...

I will be very grateful if someone could explain to me the following, in the most simple terms, f being a wave function : " ...f = f(x–ct). Let me explain the minus sign and the c in the argument. Time and space are interchangeable in the argument, provided we measure time in the ‘right’ units...

My question about the double slit experiment is this: why is it that nobody suspects that the detectors used to detect particles as they pass through the slits in the double slit experiment aren't causing some interference with the experiment which makes it seem as though they are acting like...

The wave function is an exponential function, if I plot the real part of it, I don't get a wave graph like sine or cosine function, Why the wave function is not represented by a trigonometric ratio instead. Also, the wave function cannot be plotted since it is imaginary, why is it imaginary? Thanks

Hi! For the probability interpretation of wave functions to work, the latter have to be square integrable and therefore, they vanish at infinity. I'm reading Gasiorowicz's Quantum Physics and, as you can see in the attached image of the page, he works his way to find the momentum operator. My...

Hi all, Whew, last question for a while: I think I already know the answer, but want to confirm (e..g, I think this thread basically answers the question, https://www.physicsforums.com/threads/propagation-of-wavefunction.152053/) As an example, let's say I have an electron (in free space or...

Given that we can satisfy the wave equation with a simple sine & cosine wave function (the real part of the complex wave function) in classical mechanics, why do we use the complex wave function in EM theories? In QM it is obvious that it gets more mathematically more consistent. Out of curiosity.

I was looking for questions to practice normalizing a wave function, so I visited the following online pdf, http://people.physics.tamu.edu/syeager/teaching/222/hw1solution.pdf. The first question was to find the normalization constant, A of ψ(x) = A cos (2πx/L) for (−L/4) ≤ x ≤ (L/4). After...

Hi all, I am reading something on wave function in quantum mechanics. I am thinking a situation if we have particles distributed over a periodic potential such that the wave function is periodic as well. For example, it could be a superposition of a series of equal-amplitude plane waves with...

If the problem is just to avoid negative probabilities, then why isn't the modulus of the value of wave function equal to the probability of finding the particle? I mean, is it proved by mathematics that the integration of the square of wave function value over a particular region is equal to...

Hi. Different interpretations of QM have different opinions about the ontology of the wavefunction, i.e. if it really, physically exists or if it is "just" a mathematical tool needed to calculate the outcome of measurements. The QM interpretations comparison table on Wikipedia summarises the...

I am studying about SHM but I don't know how to find an amplitude,velocity,acceralation of motio. I know the formula but I don't understand where it came from x = Asin(omega(t))

Everybody knows what is the Wave Function is. $$\Psi=\space e^{i(kx-\omega t)}$$ or $$\Psi=\space cos{(kx-\omega t)} \space - \space isin{(kx-\omega t)}$$ But can anyone tell me how it is derived. Since Schrodinger Equation is derived so easily using this Wave Function. I think it is necessary...

Hello! So if I want to describe dΨ(x)/dt can I use 1D wave equation?

Homework Statement Particle is in a state with wave function \psi (r) = A z (x+y)e^{-\lambda r}. a) What is the probability that the result of the L_z measurement is 0? b) What are possilble results and what are their probabilities of a L^2 measurement? c) What are possilble results and what...

Hi! I'm currently studying Griffith's fantastic book on QM, and I'm confused for a bit about the wave function for a free particle. Here's what I think so far; for a free particle, there are no stationary states, so therefore we can't solve the SE with...

Supposed, hypothetically, the wave function was real (Bohmians or Many World wise) and there was an "object" (or whatever) that can disrupt wave function. If you have a table and you activate the device and it destroys the wave function of the table. What would happen to the table? I just want...

1.what is the difference between radial wave function(R),radial probability density(R^2) and radial probability function(4*π*r^2* R^2)?

Is the wave function physical ? I've searched for this on the web, and most people seem to agree that it does not represent a physical thing. It'd be just a probability distribution. There is still debate and uncertainty about that question though. What annoys me then is what about the observed...