Wave function Definition and 878 Threads

If I'm trying to solve the problem of a particle in free space (H = P2/2m ). the eigenfunctions of the Hamiltonian cannot be normalized. now assume I have a legitimate wave function expressed in terms of the eigenfunction of H and I want to measure its energy. what will happen to the...

As we see in this Phet simulator, this is only the real part of the wave function, the frequency decreases with the potential, so lose energy as moves away the center. we se this real-imaginary animation in Wikipedia, wave C,D,E,F. Because with less energy, the frequency of quantum wave...

Hello! I am stuck at the following question: Show that the wave function is an eigenfunction of the Hamiltonian if the two electrons do not interact, where the Hamiltonian is given as; the wave function and given as; and the energy and Born radius are given as: and I used this for ∇...

Quantum fields have wave functions that determine a particle position in space. It solves non-locality, double-slit paradox, tunnel effect, etc. What if the wave function is also in time? Won't it solve the breaking of causality at quantum level? (Delayed Choice/Quantum Eraser/Time) Not much...

OK, so I'm trying to work out a few ideas regarding locality. I've studied at the undergrad level in the past (including quantum), but with professors that slaved away at proving math constructs and never bothered to indulge in clarifying the context of any concepts, so I'm pretty weak here...

The book on quantum mechanics that I was reading says: d<x>/dt = d/dt ∫∞-∞ |ψ(x,t)|2 dx =iħ/2m ∫∞-∞ x∂/∂x [ψ∂ψ*/∂x+ψ*∂ψ/∂x]dx (1) =-∫∞-∞ [ψ∂ψ*/∂x+ψ*∂ψ/∂x]dx (2) I want to know how to get from (1) to (2) The book says you use integration by part: ∫abfdg/dx dx = [fg]ab - ∫abdf/df dg dx I chose f...

Homework Statement Hello today I am solving a problem where an electron is trapped in a potential well. I have a solved Schrodinger's Equation. I am having problems in figuring out what the wave function should be. When I solved the equation I got a complex exponential. I know I cannot use the...

Hi everyone! Sorry for the bad english! So, just a quick doubt... Does things collapse from a wave of probability into a quantum field or is the wave in the quantum field the probabilistic wave itself? An example to make it clearer: Suppose we have an atom, it enters an atom interferometer, it...

1. Homework Statement Consider a potential field $$V(r)=\begin{cases}\infty, &x\in(-\infty,0]\\\frac{\hslash^2}{m}\Omega\delta(x-a), &x\in(0,\infty)\end{cases}$$ The eigenfunction of the wave function in this field suffices...

Consider a potential cavity $$V(r)=\begin{cases}\infty, &x\in(-\infty,0]\\\frac{\hslash^2}{m}\Omega\delta(x-a), &x\in(0,\infty)\end{cases}$$ The eigenfunction of the wave function in this field suffices $$-\frac{\hslash^2}{2m}\frac{d^2\psi}{dx^2}+\frac{\hslash^2}{m}\Omega\delta(x-a)\psi=E\psi$$...

Homework Statement Given: Ψ and Φ are orthonormal find (Ψ + Φ)^2 Homework Equations None The Attempt at a Solution Since they are orthonormal functions then can i do this? (Ψ + Φ) = (Ψ + Φ)(Ψ* + Φ*)?

Homework Statement Homework Equations where The Attempt at a Solution I tried to integrate (7-32) over all values of r (i.e., from negative infinity to positive infinity) and set it equal to 1, but the result was too messy and was divergent. Am I making the right approach?

Homework Statement Find the noralization constant ##A## of the function bellow: $$ \psi(x) = A e^\left(i k x -x^2 \right) \left[ 1 + e^\left(-i \alpha \right) \right], $$ ##\alpha## is also a constant. Homework Equations ##\int_{-\infty}^{\infty} e^\left(-\lambda x^2 \right) \, dx = \sqrt...

I just confused about it.Why can't we discribe a particle just one wave function instead of wave packet(group of waves with different phase velocities)?

Can the wave function for entangled particles be solved perturbatively? Are there virtual processes involved with this? Thanks again.

Is anyone did experiment on wave function collapse in double slit experiment. Could you please share information about that, and also share research paper about that experiment. What kind of observation done here, what kind of equipment used for that?

We want to solve the equation. $$H\Psi = i\hbar\frac{\partial \Psi}{\partial t} $$ (1) If we solve the following equation for G $$(H-i\hbar\frac{\partial }{\partial t})G(t,t_{0}) \Psi(t_{0}) = -i\hbar\delta(t-t_{0})$$ (2) The final solution for our wave function is, $$\Psi(t) =...

For this problem at t=0 Ψ(x,0)=Ψ1-Ψ3 Where Ψ1 and Ψ3are the normalised eigenstates corresponding to energy level 1 and 3 of the infinite square well potential. Now for it's time evolution it will be Ψ1exp(-iE1t/ħ)- Ψ3exp(-iE3t/ħ) And taking the time given in the question the time part of the...

Homework Statement Homework Equations For this question my ans. is coming option (3) since the time part of the wave comes out to be same for both the energy states which is (-1)^(-1/8) and (-1)^(-9/8) respectively (using exp(-iEt/ħ)). But the correct option is given option (4). Am I right...

Homework Statement Determined wave function in a hydrogen atom. ## Ψ(r,θ,Φ) = A(x+iy)e^{ \frac{-r}{2a_0}}## << find A by normalization Answer of a question in my book is ## A = -\frac{1}{a_0 \sqrt{8 \pi}} (\frac{1}{2a_0})^{3/2} ## Homework Equations ## \int Ψ^*(r,θ,Φ)Ψ(r,θ,Φ) d^3r = \int \int...

Would not any real measurement taken on a complex state logically require that the results of the measurement have less information than the state? Although I’m just beginning in QM, it appears to me unsurpring that a real measurement on the complex wave function seems to collapse the wave...

Hello, I'm trying to write a wave function for a perturbed system. The original (unperturbed) wave function has two solutions for even and odd n-values, for example ##sin(n \pi x)## for even-n and ##cos(n\pi x)## for odd-n. Then, the perturbed wave function also has an even and odd solutions...

Hi. A beam of previously unpolarized or diagonally polarized doesn't create an interference pattern behind a double slit if there is a vertically and horizontally oriented polarizer behind either slit. The classical explanation is that the electric field is a vector perpendicular to the...

The question is as follows: A particle of mass m has the wave function psi(x, t) = A * e^( -a ( ( m*x^2 / hbar) +i*t ) ) where A and a are positive real constants. i don't know how to format my stuff on this website, so it may be a bit harder to read. Generally when i write "int" i mean the...

https://ps.uci.edu/~cyu/p224/LectureNotes/lecture7/lecture7html/ Does NaCl have a wavefunction? If so, is it entangled?

Homework Statement Consider a particle which is confined in a one-dimensional box of size L, so that the position space wave function ψ(x) has to vanish at x = 0 and x = L. The energy operator is H = p2/2m + V (x), where the potential is V (x) = 0 for 0 < x < L, and V (x) = ∞ otherwise. Find...

The question is; In an experimental small universe, a photon is released from a source. It continues its path as a probabilistic wave function. if it interacted with mass, we could say the wave function collapsed and observe a particle photon hitting an object. But what happens when the photon...

For the half harmonic oscillator the ground state wave function is of the form x*exp(-x^2/2) But sir how to check it's parity and with respect to with point As this function is valid for positive x only Thank you

Homework Statement The Fourier transfrom of the wave function is given by $$\Phi(p) = \frac{N}{(1+\frac{a_0^2p^2}{\hbar^2})^2}$$ where ##p:=|\vec{p}|## in 3 dimensions. Find N, choosing N to be a positive real number. Homework Equations $$\int d^3\vec{p}|\Phi(p)|^2=1$$ , over all p in the 3...

Homework Statement $$\Psi = Ae^{\frac{i}{\hbar}(px-\frac{p^2}{2m}t)}$$ where ##p = \hbar k## and ##E = \hbar \omega = \frac{p^2}{2m}## for a nonrelativistic particle. Find ##\Psi'(x',t')##, E' and p', under a galilean tranformation. Homework Equations $$\Psi'(x',t') = f(x,t)\Psi(x,t)$$ where...

Homework Statement The wavefunction at t = 0 is given by $$\Psi = N*e^{-\frac{r}{a_0}}$$ where ##r = |\mathbf{x}|##. ##a_0## is a constant with units of length. The electron is in 3 dimensions. Find the approximate probability that the electron is found inside a tiny sphere centered at the...

If a wave function could be assigned to a whole galaxy, would its mass spread along the wave? Could this account for the anomalies in our calculations for galactic spin?

I'm trying to get a sense of the current state of knowledge regarding the relationship between gravity and quantum phenomena. For example, if you had a super-sensitive gravity detector, would that count as a "measurement" in the double-slit experiment in the same way that a particle detector...

Homework Statement A transverse traveling wave on a string starts at x = 0 and travels towards x = ∞. The wave has an amplitude of 1.20 m, wavelength of 4.60 m and travels at a speed of 14.3 m/s . At time t = 0.0 s the displacement at position x = 0.0 m is 1.20 m. (b) Calculate the displacement...

When a layman like myself hears the term 'Wave function collapse' is brings to mind physical things. A wave of some sort physically getting smaller or shrinking. Obviously that's not what it is but it does sound like it. In reality, if I have it right it's just a fancy way of saying a...

Im just starting to try to break into and understand quantum physics and so this question may be a completely absurd but I am curious as to whether or not its been proven that a particle really does act like a wave until observed or if the "spin" of two entangled atoms actually changes opposite...

Homework Statement Find the wave packet Ψ(x, t) if φ(k) = A for k0 − ∆k ≤ k ≤ k0 + ∆k and φ(k) = 0 for all other k. The system’s dispersion relation is ω = vk, where v is a constant. What is the wave packet’s width? Homework Equations [/B] I solved for Ψ(x, t): $$\Psi(x,t) =...

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...

Hi everyone, I'm kind of new in the QM world and I'm having difficulties understanding the superposition and the measurement principles together with the have function collapse. This is how I understand these principles: Superposition: While not measuring, the particle is in a superpsotion of...

I would like to get your ideas on what Australian professor at ANU David Chalmers' proposes that consciousness arises out of certain configurations of complex states (Integrated information theory) and then the existence of that consciousness collapses the wave function. Specifically, why isn't...

These are from Griffith's: My lecture note says that I am having quite a confusion over here...Does the ##\Psi## in the expression ##\langle f_p|\Psi \rangle## equals to ##\Psi(x,t)##? I understand it as ##\Psi(x,t)## being the component of the position basis to form ##\Psi##, so...

Is there a difference between Schrodinger's equation and the wave function? In the beginning of the second edition by David J. Griffiths he compares the classical F(x,t) and Schrodinger's equation and I am having trouble understanding the connection.

Homework Statement I have the wave function Ae^(ikx)*cos(pix/L) defined at -L/2 <= x <= L/2. and 0 for all other x. The question is: A proton is in a time-independent one-dimensional potential well.What is the probability that the proton is located between x = − L/4 and x = L/4 ? Homework...

Hi, I am going around in circles, excuse the pun, with phasors, complex exponentials, I&Q and polar form... 1. A cos (ωt+Φ) = Acos(Φ) cos(ωt) - Asin(Φ)sin(ωt) Right hand side is polar form ... left hand side is in cartesian (rectangular) form via a trignometric identity? 2. But then...

Hello, I am wondering if it is possible to determine the kinetic energy and potential energy of a quantum system just by investigating the graph of its wave function. Suppose we are given the graph of some wave function Ψ(x), i.e. a function which is an eigenfunction of the hamiltonian. I think...

So there's a free particle with mass m. \begin{equation} \psi(x,0) = e^{ip_ox/\hbar}\cdot\begin{cases} x^2 & 0 \leq x < 1,\\ -x^2 + 4x -2 & 1 \leq x < 3,\\ x^2 -8x +16 & 3 \leq x \leq 4, \\ 0 & \text{otherwise}. \end{cases} \end{equation} What does each part of the piecewise represent...

Hope, I do not violate any forum rules here, this is not a discussion topic, mostly. I am just asking for help looking for a specific article/work. I just remember reading somewhere that there is a QM theorem or article saying smth. in a sort that if the same physical "ontic" state would be...

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...

Homework Statement Show that the displacement D(x,t) = ln(ax+bt), where a and b are constants, is a solution to the wave function. Homework Equations I'm not sure which one to use: D(x,t) = Asin(kx+ωt+φ) ∂2D/∂t2 = v2⋅∂2D/∂x2 The Attempt at a Solution I'm completely lost on where to start...

Why is it that bosons (particles having symmetric wave functions) have integral spins and fermions (particles having antisymmetric wave functions) have half integral spins? A lot of books state this without specifying the reason. I was wondering if this is a theoretical deduction. Or is it an...