Wavefunction Definition and 585 Threads

Homework Statement Using the equations given, show that the wave function for a particle in the periodic delta function potential can be written in the form ##\psi (x) = C[\sin(kx) + e^{-iKa}\sin k(a-x)], \quad 0 \leq x \leq a## Homework Equations Given equations: ##\psi (x) =A\sin(kx) +...

Homework Statement Random given wavefunction,say $$\Psi (x) = N e^{- \mu x}$$ in a V(x) e.g. infinite well .Find ## \Psi (x,t) ##. Homework Equations - The Attempt at a Solution If the wavefunction is given as the sum of eigenfunctions,you just multiply them by ## e^{-i...

Homework Statement See Image, Sorry Its easier for me to attach images than writing all equation on the forum's keyboard! I only need to check if I'm working it out correctly up to the position expectation value because I don't want to dive in the rest on wrong basis ! Homework Equations...

I was reading Peskin&Schroeder's QFT book, and there was some discussion about how ##\left|0\right>##, the ground state of a free field and ##\left|\Omega \right>##, the ground state of an interacting field differ from each other, and they outlined how the latter can be obtained by propagating...

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...

The wavefunction describes the state of a system. When an operator 'acts on' the wavefunction are we saying, in layman's terms, that the operator is changing the state of the system?

Suppose I want to measure the momentum of a quantum system. What I do is I take the momentum operator and expand my wavefunction in term of the eigenfunctions of that operator, then I operate on the wavefunction with the operator and the reusult of the measurment is that the wavefunction...

Hi, I am a physics student and i was asked to answer some questions about Hydrogen atom wavefunctions. I hope you can help me (sorry for my english, is not my motherlanguage, i will try to explain myself properly) 1. In order to find hamiltonian eigenfunctions of Hydrogen atom, we make then be...

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...

Hi, I'm trying to work my way through some problems and am stuck on one for a symmetric infinite square well, of width 2a, so -a<x<+a. Since this is the symmetric case, the wavefunction should be a linear combination of the terms (a)-½ cos (nπx/2a) for odd n, (a)-½ sin (nπx/2a) for even n...

If you have a multi-electron atom and you swap two electrons around, what happens to the wavefunction? I think nothing happens because electrons are identical, but then they can have different spins, so would the wavefunction change if you swapped a spin up electron with a spin down one?

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...

According to theory, after any measurement the wavefunction spreads as a sphere at the speed of light from those last measurement coordinates. Since the speed of light can be slowed down by material mediums and by gravitational space warping, does that imply that the wavefunction in a material...

Homework Statement Suppose we have a wavefunction with n=4. If we measure the orbital angular momentum along the z-direction(no spin in this problem) and get 2*hbar then what are the possible values of the total angular momentum and what is the most general wavefunction after the measurement...

Layman here. It is often said that the pure fundamental theories do not contain any arrow of time, they are fully reversible in time. But regarding Shrodinger's equation, it describes the evolution of the wavefunction in time. As I understand it, if we consider a static particle after a...

In QM, we all know that the wavefunction ψ is zero when x is infinite. However, Is dψ/dx also zero when x is infinite? And the d2ψ/dx2?

Homework Statement Consider the following potential, which is symmetric about the origin at ##x=0##: ##V(x) = \begin{cases} x^{2}+(x+\frac{d}{2}) &\text{for}\ x < -d/2\\ x^{2} &\text{for}\ -d/2 < x < d/2\\ x^{2}-(x-\frac{d}{2}) &\text{for}\ x > d/2 \end{cases}## Find the ground state energy...

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...

Hi everybody, I was reading about the free particle in a textbook and I got confused by the line: "If we adopt the convention that k and k are real, then the only oscillating exponentials are the eigenfuntions with positive energy" [Also see the attached picture with the...

Homework Statement [/B] I found a couple of assignements for a physics course I will take later this year- so I started looking into them a bit in advance. It concerns wavefunctions. I'm a bit rusty on my trigonometric identities So I would love if someone could try to help me solve these two...

Can the basic techniques of wavefunction matching that one would use to calculate the transmission through a step barrier potential and the Dirac hamiltonian of graphene be used for a situation where instead the fermi velocity changes in a step like fashion. i.e. instead of a Hamiltonian like...

I think this is probably a very basic question: why does the Fourier transform of a wavefunction describing position probabilities gives us a function describing momentum probabilities ? Is there a fairly simple explanation for this ? What leads us to this relation ?

Suppose we measure a normalized state ##|\Psi \rangle = \alpha _0 | \lambda _0 \rangle + \alpha _1 | \lambda _1 \rangle + \alpha _2 | \lambda _2 \rangle + ...## with ##| \lambda _i \rangle## the eigenvalues of the measured observable. Is it true that, in the CI, the wavefunction collapses into...

I'm facing some difficulties in using "boundary conditions" in a simple wavefunction. The wavefunction I'm considering is $$\xi(x,t)=A sin (k x \pm \omega t +\psi)$$ The minus or plus are for progressive or regressive waves. The indipendent parameters are 4: ##A##, ##k##, ##\omega##, ##\psi##...

Homework Statement A sinusoidal wave on a rope with linear density ##\mu=0.012 kg/m## is described in SI units by $$\xi(x,t)=A sin (kx-\omega t)= 0.15sin(0.8x-50t)$$ a) find the maximum acceleration of a rope element b) find the maximum transverse force on a piece of rope ##1 cm## long c) Show...

Hi, guys. If I want to write the spin-flavor wavefunction of ##\Sigma_+## starting only from knowing that the quark content of the proton is ##uud##, how can I procced? I started by applying the ladder operators in order to get the baryon octet vertexes. I am now having problems with...

Homework Statement [/B] Consider an ideal rope where there is a wave moving at velocity ##v=20 m/s##. The displacement of one end of the rope is given by $$s(t)=0.1 \mathrm{sin}(6 t)$$ a) Find the wavefunction ##\xi(x,t)##, knowing that it is progressive b) Find the distance ##\delta## (in...

Hi everybody. I was reading about the singlet and triplet states. It makes sense that we use an antisymmetric wavefunction for the singlet state, as we are talking about two fermions. But why are we using a symmetric wavefunction for the Sz = 0 triplet state? Doesn't this go against the...

I learned that the moment a wavefunction collapse takes place is a matter of interpretation. So, I suppose the phenomenon 'wavefuntion collapse' is something that has to be witnessed by observation at some point to be able to establish it at all! So my question is: if collapse doesn't actually...

Hi all! Consider a wavefunction, where ##\left| \psi (x) \right|^2 = e^{-ax^2+1}+e^{-bx^2-1}## where a and b are real, positive numbers that satisfy normalization (they are purpously inside the exponent). Even if it is normalized, there are still 2 spots that ##\left| \psi \right|^2 > 1## which...

Or is it a physical property of the quantum system? Or else? The Joint Committe fo Guides in Metrology: http://www.bipm.org/en/committees/jc/jcgm/ says that: "A physical quantity (or "physical magnitude") is a physical property of a phenomenon, body, or substance, that can be quantified by...

From the Theory of Open Quantum Systems; the Euler scheme is given by: ##\psi_{k+1} = \psi_{k} + D_1(\psi_k)\Delta t + D_2(\psi_k) \Delta W_k## and is a scheme of order 1. What does the order of convergence mean? From my understanding higher order schemes require fewer interations to give a...

Homework Statement Given the following wave function valid over -a \le x \le a and which is 0 elsewhere, \psi(x) = 1/\sqrt{2a} Find the uncertainty in \left<\left(\Delta p\right)^2\right> momentum, and the uncertainty product \left<\left(\Delta x\right)^2\right>\left<\left(\Delta...

Hi guys, I saw mr. Nugatory's post on one of the older threads which got me a bit conceptually confused so I wanted to ask you a question regarding it. This is the original quote: "For most macroscopic systems most of the time, the wave function evolves in a way that makes quantum effects like...

Hello! It is sometimes useful to find the average energy of a certain number N of particles contained in a box of volume V. In order to find this quantity, the total energy is required and then divided by N. The result is E_{average} = \displaystyle \frac{1}{N} \sum_{n = 1}^{N} \left| a_n...

Homework Statement the wavefunction where <|> = . I want to normalize it and find constant normalization A. A is real number. Homework EquationsThe Attempt at a Solution I know that for normalizing the wave function but what happen for sigma? can I remove it from equation?

1. Homework Statement We are studying circular states of the hydrogen atom (states where the l quantum number is = n-1). We are asked to evaluate \langle \Psi_{n,n-1,n-1}| r_{n,l=n-1}|\Psi_{n,n-1,n-1}\rangle . The wave function is that of the hydrogen atom, and the thing we are taking the...

It's my first post so big thanks in advance :) 1. Homework Statement So the question states "By interpreting <pxΨ|pxΨ> in terms of an integral over x, express <Ekin> in terms of an integral involving |∂Ψ/∂x|. Confirm explicitly that your answer cannot be negative in value." ##The 'px's should...

Everywhere I ready about HF or DFT the term exchange correlation functional comes up. I have a couple of fundamental questions about these: 1) Books say that the correlation energy is the difference between the exact energy (lets say we've found that somehow) and the hartree-fock energy and...

Hi pf, I am having trouble with understanding some of the steps involved in a mathematical proof that a normalized wavefunction stays normalized as time evolves. I am new to QM and this derivation is in fact from "An introduction to QM" by Griffiths. Here is the proof: I am fine with most of the...

EDIT: moved from technical forum, so no template Hello, I have a problen which is about calculating an electrostatic potential for a hydrogenic atom in the ground state given its wavefunction. Since I know the wavefunction of the ground state I would find it by solving the Schrödinger...

The thread title is probably confusing, but I couldn't really think of a better one. There is a basic feature of quantum mechanics that I have been puzzled by for a long time. My guess is that my issue stems from some fundamental misunderstanding of the theory, so I would appreciate any efforts...

I Have a question about how we arrive at the probabilities for the wavefunction collapsing to some specific value for an observable. As far as I'm aware, the wavefunction is a superposition of possible states depending on the observable we try to measure. Lets say I want to measure observable...

The wavefunction ##\Psi(x,t)## for a free particle is given by ##\Psi(x,t) = A e^{i(kx-\frac{\hbar k}{2m}t)}## This wavefunction is non-normalisable. Does this mean that free particles do not exist in nature?

I have been told on another forum I post to that there is a revolutionary theorem in physics which proves beyond doubt that the wavefunction (I presume meaning the one originally described by Schrodinger) is physically real. I have had various exchanges with the contributor who has told me this...

Upon a measurement of the position, the wavefunction collapses to a spike centered at x0 https://farside.ph.utexas.edu/teaching/315/Waveshtml/img3240.png I encounter similar spike pictures numerous times, but there is an uncertainty in position , it can't be a spike right. First thing I see...

Hello, I have the following problem: A system in the lab frame is described by a time dependent rotating potential ##V(\vec{r},t)##. So ##H_{lab}=\frac{\boldsymbol{p}^{2}}{2m} + V(\vec{r},t)##. My book says that the Hamiltonian in the rotating frame is given by...

How do you know when to use exponentials and trig functions when solving for the wave function in a finite square well? I know you can do both, but is there some way to tell before hand which method will make the problem easier? Does it have something to do with parity?

Hi, I am wondering how to plot a complex function of the form: Ψ(t) = Ansin(n⋅pi⋅x/L)e-iEnt/h + Bnsin(m⋅pi⋅x/L)e-iEmt/h + ... + where m and n are known eigenvalues of the infinite square well with corresponding energy En, for any particular x? So, this will be a function of solely t. Any help...

In interpretations where the wave function is real, what does that mean? does it mean that the wave function has physical meaning?