Wavefunction Definition and 572 Threads

I need to know what is the typical extention of the (spatial) wavefunction of an atomic nucleus in a crystal, in particular I am interested to the case of a Germanium cristal. Please together with the actual number of the size of the nuclei wavefunctions, let me know the references (articles or...

Having in mind the idea that "information is not lost" (referring to the black hole information paradox), is not the same rule violated in the wave function collapse? I.e. during the decoherence process information is not lost as this process of entanglement of some object with its environment...

I was solving an exercise from Cohen's textbook, but then I got stuck in this question. "Let ψ(x,y,z) = ψ(r) the normalized wave function of a particle. Express in terms of ψ(r) the probability for: b) a measurement of the component Px of the momentum, to yield a result included between p1...

Homework Statement The Attempt at a Solution [/B] Hi All, I'm having trouble answering part (f) of the above question. I have managed parts (d) and (e) fine but am not sure how to proceed with part (f). I am pretty sure that the amplitude of the reflected wave in region 1 will be zero...

If I understand it correctly, a particle doesn't have a definite momentum and a definite position, but is in a superposition of multiple positions and momenta. And when we measure either of the two quantities, say, position, the wavefunction collapses to tell us where the particle is. Now when...

Imagine a system of 1 particle in a superposition of eigenstates of some operator(s). If one were to make a measurement of a property of that particle, how is the operator (or observable) "picked" so that the wavefunction collapses into an eigenstate of said operator? In other words, how do one...

For the harmonic oscillator, I'm trying to study qualitative plots of the wave function from the one-dimensional time independent schrodinger equation: \frac{d^2 \psi(x)}{dx^2} = [V(x) - E] \psi(x) If you look at the attached image, you'll find a plot of the first energy eigenfunction for...

Suppose you have an experiment that measures the property of an atom as a whole, maybe you can put it through a double-slit or measure its spin, whatever. Presumably that will collapse the wavefunction that you used to describe the atom in that experiment. Would this entail that in the process...

In ab initio calculations for periodic systems, only an irreducible K grid is used for calculation, and consequently only those K points have their wavefunction calculated. My question is, how to recover wavefunction at other K points not included in the irreducible K grid? Similar questions to...

Hi physicsforums, I am an undergrad currently taking an upper-division course in Quantum Mechanics and we have begun studying L^2 space, state vectors, bra-ket notation, and operators, etc. I have a few questions about the relationship between L^2, the space of square-integrable complex-valued...

Hello, My understanding is that, for a multi-particle system, the overall wavefunction HAS to be either symmetric or antisymmetric. A wavefunction that is neither symmetric or antisymmetric must be converted into one that is one of the two types depending on the type of particles. For example...

Okay, so I've been set this homework to find the normalisation constant, N, for the radial wave function in the 2s state for hydrogen (my title was too long to fit that vital information in). thing is; I'm having a bloody hard time and in the process confusing myself with trying to take out all...

Hi! I would like to wrap my head around a relatively simple issue. Lets say that you have an excited atom, which rests in your refernce frame. When it emits light, the atom will have a backreaction, and it will "gain momentum" with the opposite direction as the photon. Of course, without...

Hi, are there any models known in QM where the wavefunctions do not have to be infinitely differentiable, and thus can exist in other spaces than the Hilbert space? I assume Banach spaces allow elements that are not infinitely differentiable as subsets. Can therefore certain phenomena in QM be...

I was wondering if anyone has worked with non-Hermitian wavefunctions, and know of an approach to derive real and trivial values for their observables using numerical calculations? Cheers

Hi, in Bohm's "Quantum Theory" David Bohm writes: for n-particles the wavefunction is:\begin{equation} G (_{N}) = Ae^{ip \eta /\hbar} + B e^{-ip \eta /\hbar} \end{equation} But this is the same as a wavefunction in one dimension (x) given in Atkins and Friedman "Molecular Quantum Mechanics"...

This problem bothered me many years ago when I was taking a university course in quantum mechanics, but I assumed it was due to an error on my part which I, however, couldn’t locate, and I didn’t ask my course instructor about it. Recently, when researching a q.m. question on the Internet...

Hi. My question is a general one but I will use an infinite well as an example. Without knowing details of the exact wavefunction I presume it can exist as a linear superposition of an infinite number of energy eigenstates ? Without knowing the exact wavefunction ; does that mean that when the...

Hi, I have heard (or imagined) that a wavefunction, where Psi is on the y-axis and the positions x is naturally on the x-axis, is really a one-dimensional system in Physics (not in mathematics), because the signal or the oscillation of the wavefunction is not really a dimension, and only the...

Homework Statement A particle is restrained to move in 1D between two rigid walls localized in ##x=0## and ##x=a##. For ##t=0##, it’s described by: $$\psi(x,0) = \left[\cos^{2}\left(\frac{\pi}{a}x\right)-\cos\left(\frac{\pi}{a}x\right)\right]\sin\left(\frac{\pi}{a}x\right)+B $$ , determine...

Homework Statement Find relation between real normalisation constants ##B_1## and ##B_2## for the following wavefunction, $$ \Psi_k =\sum_{k=1,2} \frac{B_k}{\sqrt{4\sigma ^2 + 2it}} \exp (ip_k (x - \frac{p_k}{2}t) - \frac{(x - p_k t)^2}{4\sigma ^2 + 2it}) $$ The working is rather long so...

Hello, I Have a non-Hermitian Hamiltonian, which is defined as an ill-condition numbered complex matrix, with non-orthogonal elements and linearily independent vectors spanning an open subspace. However, when accurate initial conditions are given to the ODE of the Hamiltoanian, it appears to...

Say you have two particles a and b with respective positions ##x_a## and ##x_b##. Particle a is in the state ##\psi_a##, and particle b is in the state ##\psi_b##. If they are distinguishable, the wavefunction is $$\psi=\psi_a(x_a)\psi_b(x_b)$$ However, if they are identical fermions, the...

Hi, I am working on a home-task to analyse the properties of a ODE and its solution in a Hilbert space, and in this context I have: 1. Generated a matrix form of the ODE, and analysed its phase-portrait, eigenvalues and eigenvectors, the limits of the solution and the condition number of the...

Hi. Is the wavefunction for x≤0 , ψ(x) = sinkx - acoskx equivalent to ψ(x) = -sinkx - acoskx where a is a constant ? Thanks

Hello, I Have a particle with wavefunction Psi(x) = e^ix and would like to find its Hilbert space representation for a period of 0-2pi. Which steps should I follow? Thanks!

Homework Statement I've been asked as a part of some school project to find the Fourier transform, and time evolution of the following initial wavefunctions: 1. ##\Psi(x,0) = Ae^{\frac{-x^2}{2\sigma ^2}}## 2. ##\Psi(x,0) = Be^{\frac{-x^2}{2\sigma ^2}}e^{\frac{ipx}{\hbar}}## What physical...

I have 2 questions i would really like to find an answer to: if we have a quantum pair, we can determine whether 2 quanta are entangled or not assuming that we have access to the information of both of them. so if we have a quantum "trio" instead of a quantum pair, does the information about 2...

Is it true that by multiplying wavefunction with arbitrary complexnumber, which module is 1, results another wavefunction, that has same physical meaning? aka ##\forall_\phi(\Psi\ has\ the\ same\ meaning\ as\ \Psi \cdot e^{i \cdot \phi})## If not please give me an example of wavefunction and...

Homework Statement Consider the wavefunction: Ψ(x, t) = Ae-λ|x|e−iωt Normalise Ψ(x, t) Homework Equations ∫ |Ψ(x, t)|2 dx = 1 (bounds from x: -∞ to +∞) The Attempt at a Solution Ψ(x, t) = Ae-λ|x|e−iωt Ψ(x, t) = Ae-λ|x|−iωt Ψ*(x, t) = Ae-λ|x|+iωt ∫ |Ψ(x, t)|2 dx = A2 ∫...

Homework Statement [/B] Determine the value that A (assumed real) must have if the wavefunction is to be correctly normalised, i.e. the volume integral of |Ψ|2 over all space is equal to unity. Homework Equations Integration by parts (I think?) The Attempt at a Solution So, I've managed...

Homework Statement I have a few questions I'd like to ask about this example. (C1 was already derived before the second part) 1. What does the line "The rest of the coefficients make up the difference" actually mean? 2. What does "As one might expect...because of the admixture of the...

The wave packet or wave function that spreads in time is one reason Schrodinger didn't make it as the particle itself.. and the death of wave particle duality. Also why Born introduced the probability distribution. For those of us who are Many worlder with their emphasis of the wave function as...

1)Is the wave function of the electron perpendicular to the motion of electron in straight line in the similar fashion as that of the photons.? 2) And what is the origin of this wave function? 3) can someone give me the details about the electron in double slit experiment (and mainly a theory...

Homework Statement ## \psi(x) = N. (x^2 - l^2)^2 ## for ##|x| < l , 0 ## otherwise We have to find N such that this wavefunction is normalised.2. The attempt at a solution I tried expanding the ## (x^2 - l^2)^2 ## term inside the integral but this integral is extremely messy : ##...

What are the experiments that disprove the idea that consciousness causes wavefunction collapse?

I think we can all agree that when we are shooting many photons one by one, through an interferometer, we can eventually land up with the interference pattern. This can be explained by saying that two photons combining in some areas to give four photons and in some places annihilating each...

Hello, I've noticed that some professors will jump between second quantized creation/annihilation operators and wavefunctions rather easily. For instance \Psi_k \propto c_k + ac_k^{\dagger} with "a" some constant (complex possibly). I'm fairly familiar with the second quantized notation, and...

In some sources QM is explained using bracket notation. I quite understand algebra of bracket notation, but I do not understand how is this notation related with physically meaningful things? How is bracket notation related to wavefunction notation? Could you tell me whether following is true...

Hello! I have a proof in my QM book that: ##\left<r|e^{-iHt}|r'\right> = \sum_j e^{-iHt} u_j(r)u_j^*(r')##, where, for a wavefunction ##\psi(r,t)##, ##u_j## 's are the orthonormal eigenfunctions of the Hamiltonian and ##|r>## is the coordinate space representation of ##\psi##. I am not sure I...

the spin, S, for an electron is $$\frac{\hbar}{2}=5.27 \cdot 10^{-35} $$ $$\frac{2MR^2 \omega}{5}=\frac{2MRv}{5}$$ It is said that the speed of an electron is 2200 km per second and can be calculated in classical manners from electrostatic and accelerating forces on the electron from (1.11)...

so I am finishing up my studies of intro to quantum mechanics, and this is not in my book and looking at previous exams i have to know this for single electron atoms/ions. one of the problems was somethin like "the wave function of an electron is the overlap of the orbitals: Ψ=aΨ1s+i/√3Ψ2p+¾Ψ3s...

Q1. Why is the probability current ##j(x,t)=0## at ##x=\pm\infty##? (See first line of last paragraph below.) My attempt at explaining is as follows: For square-integrable functions, at ##x=\pm\infty##, ##\psi=0## and hence ##\psi^*=0##, while ##\frac{\partial\psi}{\partial x}## and hence...

We know that in one dimension if ##E>V(\infty)## or ##E>V(-\infty)## then the resulting wave function will not be normalizable. The basic argument is that if ##E>V(\infty)##, then a stationary solution to the Schrodinger equation will necessarily have a concavity with the same sign as the...

Two Questions from a newbie. A) Is there a easily implemented process or reaction that results in a particle with reciprocal wave function of input particle? B) Is there a easily implemented process or reaction that results in a particle A transferring it's wavenumber and angular frequency to...

What is the wave function? does it have several different forms? how does the Schrodinger equation compare to the wave function?

I'm trying to prove that the wave function of Hydrogen for the fundamental state is normalized: $$ \Psi_{1s}(r)=\frac{1}{\sqrt{\pi a^3}}e^{-\frac{r}{a}} $$ What I tried is this: $$ I= \int_{-\infty}^{\infty} | \Psi^2(x) | dx = 1$$ $$ \int_{-\infty}^{\infty} \frac{1}{\pi...

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...

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

Hi all, I would like some thoughts on the following quote I read from a book on the history of QM: "Quantum: Einstein, Bohr, And the Great Debate About the Nature of Reality." Please restrict your consideration to the Bohr/Heisenberg 'Copenhagen' interpretation (I realize in other...