Wave function Definition and 878 Threads

(a) Let the center of the concentric spheres be the origin at ##r=0##, where r is the radius defined in spherical coordinates. The potential is given by the piece-wise function $$V(r)=\infty, r<a$$ $$V(r)=0, a<r<R$$ $$V(r)=\infty, r<a$$ (b) we solve the Schrodinger equation and obtain...

For the sake of this question, I am primarily concerned with the position wave function. So, from my understanding, the wave function seems to 'collapse' to a few states apon measurement. We know this because, if the same particle is measured again shortly after this, it will generally remain in...

The wave function ψ(x) of a particle confined to 0 ≤ x ≤ L is given by ψ(x) = Ax, ψ(x) = 0 for x < 0 and x > L. When the wave function is normalized, the probability density at coordinate x has the value? (A) 2x/L^2. (B) 2x^2 / L^2. (C) 2x^2 /L^3. (D) 3x^2 / L^3. (E) 3x^3 / L^3 Ans : D

I am having a trouble to understand why the helium's wave function (in which we are ignoring the electric interaction between the electrons, as well the motion and problems that arise in considering the nucleus in the wave function) can be written as the product of the wave function of both...

I know how to work through this problem but I have a question on the initial separation of the wave function. Assuming ##\psi(\rho, \phi) = R(\rho)\Phi(\phi)## then for the azimuthal part of the wavefunction we have ##\Phi(\phi)=B\left(\frac \rho\Delta cos\phi+sin\phi\right)##, but this function...

It is a rather simple question: In my textbook it writes something like: $$\frac {\partial \Psi} {\partial t}= \frac{i\hbar}{2m}\frac {\partial^2 \Psi} {\partial x^2}- \frac{i}{\hbar}V\Psi$$ $$\frac {\partial \Psi^*} {\partial t}= -\frac{i\hbar}{2m}\frac {\partial^2 \Psi^*} {\partial...

We know that the non-relativistic propagator describes the probability for a particle to go from one spatial point at certain time to a different one at a later time. I came across an expression (lecture notes) relating ##\Psi(x,t)##, an initial wave function and the propagator. Applying the...

Reading the classical Feynman lectures, I encounter the formula(19.53) that gives the radial component of the wave function: $$ F_{n,l}(\rho)=\frac{e^{-\alpha\rho}}{\rho}\sum_{k=l+1}^n a_k \rho^k $$ that, for ##n=l+1## becomes $$ F_{n,l}=\frac{e^{-\rho/n}}{\rho}a_n\rho^n $$ To find ##a_n## I...

The question arose when watching Sean Carroll video: The Biggest Ideas in the Universe _ Q&A 6 - Spacetime 3:50 - 13:30 Because photons follow null geodesic in spacetime the question arose from viewers: "photons do they really experience no time this is a question" And in the answer: "but if...

When studying classical mechanics we are told that light is the propogation of electromagnetic waves. This makes perfect sense, as I can imagine these fields behaving this way, and in turn have an associated wave length. When learning about QM, I have heard that the wavelength of a (any)...

I was wondering if it's possible to plot a wave function that is a function of 3 coordinates, such as (x, y, z). The text my class uses calls this Quantum Mechanics in 3 dimensions, but wouldn't this technically by four dimensions?

I read about the non-communication theorem and I understand why when changing one practical will not change the other . But suppose that there is two observers that doing the double slit experiment, but using it with two entanglement practicals. observer one should send signal of yes or...

For part a, I have the following $$\ket{p_0} = \varphi_{p_0}(x)=\frac{1}{\sqrt{2\pi\hbar}}e^{ip_0x/\hbar}$$ but I am totally lost on how to proceed.

I've been studying quantum mechanics this semester in school and have ran into an issue I can't find an answer for. I understand why we take the complex conjugate of the wave function, such as when calculating expectation values. I'm a little confused though as to why we take the complex...

I am trying to solve the following exercise. In a H atom the electron is in the state described by the wave function in spherical coordinates: \psi (r, \theta, \phi) = e^{i \phi}e^{-(r/a)^2(1- \mu\ cos^2\ \theta)} With a and \mu positive real parameters. Tell what are the possible values...

In QM by virtue of wave function we calculate any things. But in QFT it seems that there is a lacking of notion of wave function.I do not understand why QFT still goes well(it is a good theory to calculate any things)?

https://phys.org/news/2020-09-function-collapse-gravity.html An interesting article I saw yesterday. However, both Nature articles (the summary [https://www.nature.com/articles/s41567-020-1026-2] and the actual technical paper [https://www.nature.com/articles/s41567-020-1008-4]) are behind a...

I never took any physics courses nor don't have a background in mathematics never the less I became very interested in quantum physics after reading Sean Carroll's book Something deeply hidden. One of the difficult things for me to wrap my head around was the concept of superposition and...

I have a basic question in elementary quantum mechanics: Consider the Hamiltonian $$H = -\frac{\hbar^2}{2m}\partial^2_x - V_0 \delta(x),$$ where ##\delta(x)## is the Dirac function. The eigen wave functions can have an odd or even parity under inversion. Amongst the even-parity wave functions...

I don't see why it is not ##P(\omega)\propto |\langle \psi | \mathbb{P}_{\omega}|\psi\rangle |^2.## After all, the wavefunction ends up collapsing from ##|\psi\rangle## to ##\mathbb{P}_{\omega}|\psi\rangle.##

When wave function collapses how long is it collasped... Shooting electrons at a double slit and observing the electrons before they reach the 2 slits collasped the wave function...so is its behavior particle like forever? Quantum mechanics is simple however wrapping ones head around it is...

Hello! I have been recently studying Quantum mechanics alone and I've just got this question. If the potential function V(x) is an even function, then the time-independent wave function can always be taken to be either even or odd. However, I found one case that this theorem is not applied...

May i know how do i eliminate C and D and how do i obtain the last two equations? Are there skipping of steps in between 4th to 5th equation? What are the intermediate steps that i should take to transit from 4th equation to the 5th equation?

hello , hope all of you are doing well , i have question about the unit of the function of waves of string fixed in both boundary , the function of waves is function of two variables x and t , so it's function describe the displacement in function of place and time , Ψ(x,t)=φ(x)*sin(ωt+α)...

Hello all, I am a newcomer here. Not a physicist, just an enthusiast. ;) I was thinking whether it is possible to separate a one-particle wave function into two, "completely disjoint" parts. The following thought experiment explains better what I am thinking about. Let us suppose, that there...

The book's procedure for the "shooting method" The point of this program is to compute a wave function and to try and home in on the ground eigenvalue energy, which i should expect pi^2 / 8 = 1.2337... This is my program (written in python) import matplotlib.pyplot as plt import numpy as...

Some questions: Why is this even a valid wave function? I thought that a wave function had to approach zero as x goes to +/- infinity in all of space. Unless all of space just means the bounds of the square well. Since we have no complex components. I am guessing that the ##\psi *=\psi##. If...

I was thinking about a problem I had considered a long time ago in some thread, finding an example of a wave function ##\displaystyle \psi (x) =e^{iax}\phi (x)## with ##\displaystyle\phi (x)## being periodic with period ##\displaystyle L## and the corresponding Schrödinger equation...

To plot ##u(r)## we need to find the solutions for each region. Which is in the relevant equations part. Now, I have to do this numerically. Using python 3.7 I made an ##u## which is filled with zeros and a for loop with if/elseif statement, basically telling it to plot values for whenever...

Hi, I just need someone to check over my work. I am having trouble with the next part of this question and I just wanted to check that this part was correct first. I have two particles in an infinite square well (walls at x=0 and x=L). I need write an expression for the spatial wave...

I thought I could start somewhere along the lines of ##\psi(x,t)= \psi(x,0)e^{-iE_nt/\hbar}##, but I'm not sure what ##E_n## would be. I also thought about doing the steps listed below in the picture, but I'm not sure how to decompose ##\psi(x,0)## like it says to in the first step. Any help...

I was planning to find the value of N by taking the integral of φ*(x)φ(x)dx from -∞ to ∞ = 1. However, this wave function doesn't have a complex number so I'm not sure what φ*(x) is. I was thinking φ*(x) is exactly the same φ(x), but with x+x0 instead of x-x0. Thank you

A composite object made of many atoms has a large mass hence a small de Broglie wavethength...and we know that recent experiments succeeded to obtain interference patterns even for such objects (for instance the C60 molecule). Did theoretician understood how a wavefunction with such a small...

Considering Bell’s theorem and the expected correlations between entangled particles or photons. In a measurement setup e.g. Like Alain Aspect‘s with 2 entangled photons. If we could make a setup that guarantees that the measurement on both photons is done at exactly the same moment, what...

I've been reading about Quantum Field Theory and what it says about subatomic particles. I've read that QFT regards particles as excited states of underlying quantum fields. If this is the case, how can particles be regarded as objective? It seems to me that this also removes some of the...

Summary:: Wave function of a laser beam before it hits the diffraction grating So I'm reading "Foundations of Quantum Mechanics" by Travis Norsen. And I've just read Section 2.4 on diffraction and interference. And he derives a lovely formula for the wave function of a particle after it leaves...

Hi everyone! This is the first time I'm posting on any forum and I'm still rather unsure of how to format so I'm sorry if it seems wonky. I'll try my best to keep the important stuff consistent! I am working on infinite square well problems, and in the example problem: V(x) = 0 if: 0 ≤ x ≤ a...

Given that the wave function represented in momentum space is a Fourier transform of the wave function in configuration space, is the conjugate of the wave function in p-space is the conjugate of the whole transformation integral?

Can you say whether I understood these things correctly? to get condition on wavefunction ##\Psi## for a system that consists of 2 electrons(without taking spin into account) and helium nuclei I can solve schrödinger equation: ##i*\frac{\partial \Psi}{\partial...

Born's postulate suggests if a particle is described a wave function ψ(r,t) the probability of finding the particle at a certain point is ψ*ψ. How does this work and why?

In Landau-Lifsits's book about non relativistic QM it is said that if I have a particle described by a plane wave ##\phi = e^{ikz}## (I think he choses the ##z## direction for simplicity) the wave function after the scattering event is (far from the scattering event) $$\psi \approx e^{ikz} +...

I use the equation ##\psi \left ( x, t \right ) = e^{-iEt/\hbar} \psi \left ( x,0 \right )## to calculate ##\psi \left ( x , t \right)##, and the result is ##\psi \left ( x , t \right) = \frac 1 {\sqrt {2 \pi \hbar}} exp \left [ \frac {ip_0 x} {\hbar} - \frac {i p^2 t} {2m \hbar} \right...

Elementary question: Is there ever a case where the solutions for a wave equation turn out not to be a vector (in Hilbert space of infinite complex-valued dimensions, or a restriction to a subspace thereof) , but something else -- say, (higher-order) tensors or bivectors, or some such? My...

Why can't the general state, in the presence of coupling, take the form $$\psi_-(r)\chi_++\psi_+(r)\chi_-$$ where ##\psi_+(r)## and ##\psi_-(r)## are respectively the symmetric and anti-symmetric part of the wave function, and ##\chi_+## and ##\chi_-## are respectively the spinors representing...

This thread is to look at the notion of wave function collapse and relativity of simultaneity. The other thread I started on QFT has helped to clarify a lot, so hopefully this one can do the same. I may have this all wrong, but I will outline my question and hopefully someone can point out...

Fermions such as the electron and proton can be described by wave function in momentum and in position, and it is possible to get the momentum wavefunction from space wave function and vice versa by Fourier Transform. what about photons? can photons be described by position wave function? If...

We always think in terms of isolated particles. It's better to analyze it with solids. If wave functions were just calculational tools. Molecules like the following still interact by wave functions, right? So how can it be calculational tool? And if it is, then what model do you use to...

In interpretations where the wave function represents something real, like Many worlds, Copenhagen with objective wave function and spontaneous objective collapses. I'd like to understand which of them has true non-locality. First. Is Many Worlds not having true non-locality due to the...

I have calculated the normalization constant, but I'm struggling with the discontinuities in the derivatives of the wave function. Due to the symmetry, it should suffice to consider the first two cases. The results should be (according to WolframAlpha): \left( \frac{\partial^{2}}{\partial...