Wave function Definition and 865 Threads

Dear PF Forum, It's been a while since I logged in. And I hope everybody is in good health. Here I have a question concerning quantum computer. First, I'm no unfamiliar with a computer. I'm a computer programmer, but I don't know any physics. How can a quantum computer be a lot faster then an...

I'm wondering about phase contrast imaging with a transmission electron microscope (TEM). It's generally accepted that phase contrast arises because scattered waves interfere with the unscattered wave when they meet again in the image plane. It's also well established, I believe, that each...

Hi, We just started studying wave-particle dualism and there is a basic thing I do not understand. Usually we use a planar wave packet to describe particles (an electron for example). This seems confusing to me because planar waves have infinitely extended wave fronts, which first of all means...

The wave function includes coordinates for position in space. For two distant but correlated particles, do their distances and paths of movement used in the wave function follow the curved space-time of general relativity, or is Euclidean distance assumed in QM?

In thinking about the particle in an infinite square well, it the commonly espoused boundary conditions of ψ(0) = 0 and ψ(L) = 0 seem somewhat arbitrary. What in nature forces the wave function to vanish at the boundaries? If the particle can't escape and there is no energy loss, why not...

Suppose we have in a box a particle that is travelling left and right at some speed, bouncing off the walls of the box. The wall on the right is then removed such that the particle would be free to escape the box. Does the wave function of the particle get "updated" instantly the moment the...

It's obvious that the Observer Effect can take place without conscious observation, for example with a photon and electron out in the wild, but I'm trying to find a single study which disproves the role of conscious measurement within the observer effect. An experiment which I think would...

People very often say the collapse of the wave functions in the discussion of quantum mechanics, then how to write this process in math form?

In Griffith's page 7, the following is mentioned: What confuses me here the most is the first sentence: "Particles have a wave nature, encoded in ##\psi##" As far as I have understood, the square of the amplitude of the wave function gives us the probability of finding a function at a...

I am meeting the momentum space wave function ##\Phi\left(p,t\right)## in chapter 3 of Griffiths & Schroeter. I have an integral which I can integrate by parts: $$\int_{-\infty}^{\infty}{\frac{\partial}{\partial p}\left(e^\frac{ipx}{\hbar}\right)\Phi d...

Hi guys i have this exercise: A particle of mass m, confined in the segment -a/2 < x < a/2 by a one-dimensional infinite potential well, is in a state represented by the wave function: 1. Determine the constant N from the normalization condition. To do this, I have to integral the square...

Hi, I'm aware of the wave function ##\Psi## of a quantum system represents basically the "continuous components" of a quantum state (a point/vector in the infinite-dimension Hilbert space) in a basis. If we take the ##\delta(x - \bar x)## eigenfunctions as basis on Hilbert space then the wave...

In answering another question, I came across a nice paper by Weinberg: https://www.arxiv-vanity.com/papers/hep-th/9702027/ One thing that struck me was the following comment: 'In its mature form, the idea of quantum field theory is that quantum fields are the basic ingredients of the...

If we take the wave function Ψ of a particle X that gets measured in a basis with a finite countable number of eigenvectors N, then according to MWI and myself, the interpretation suggests that we can write Ψ as the sum of projections of Ψ on the eigenvectors the following way: Ψ= Σn |e(n)> ⊗...

In a thought experiment one could arrange synchronized clocks in an inertial frame of reference such that they show the same time when the collapse happens. Does that mean that according to the relativity of simultaneity from the perspective of an observer in relative motion to that frame the...

If I am correct, the wave function is presented as a vector in Hilbert Space. Alternatively this vector can be multiplied by the identity operator. Is there a preference for one notation or the other? Are they both possible representations of the same wave function?

Physicist Dr. Muthuna Yoganathan thought the wave function was just a calculation tool, which is the standard minimal interpretation of QM. But then she started doing her own versions of the double-slit experiment at home using a red laser, culminating in purchasing a smoke machine. With that...

Dear all, I was reading through the book "QFT for the gifted amateur" because I'm currently working on a popular science book about symmetries. Chapter 9 is about transformations of the wave function. On page 80 the book says It's the second equality that confuses me: doesn't the statement...

Sabine Hossenfelder implies spooky action at a distance is wrong. She says “They seem to think if you do something to one particle in an entangled pair, then that will immediately affect the other one. But this isn’t so. It’s only when you measure one particle, then you have to update the...

I'm given a wave function for an electron which is given as: For an electron in this state the kinetic energy is being measured, where the kinetic energy operator is p^2/2m. How can I find the probability (density) that an electron is found to have kinetic energy in the interval [E, E+dE]? I...

TL;DR Summary: A completely non-scientific look at wave function, because ChatGPT persuaded me to include my thoughts somehow, some way. Howdy, the post title, as im sure you've noticed, is a weird one, and out of place in such a location. Fitting, considering the topic, I think. Backstory...

Say you have a simplified 1d Gaussian wave function describing location of a particle. Many worlds says that every outcome is a separate branch. Copenhagen says you will get one of those branches. So how many distinct positions, imaginary or real, can you generate from a fixed segment of a...

In the picture below we have two identical orbitals A and B and the system has left-right symmetry. I use the notation ##|n_{A \uparrow}, n_{A \downarrow},n_{B \uparrow},n_{B \downarrow}>## which for example ##n_{A \uparrow}## indicates the number of spin-up electrons in the orbital A. I would...

I've already calculated the total spin of the system in the addition basis: ##\ket{1 \frac{3}{2} \frac{3}{2}}; \ket{1 \frac{3}{2} \frac{-3}{2}}; \ket{1 \frac{3}{2} \frac{1}{2}}; \ket{1 \frac{3}{2} \frac{-3}{2}}; \ket{0 \frac{1}{2} \frac{1}{2}}; \ket{0 \frac{1}{2} \frac{-1}{2}}; \ket{1...

In this 2011 paper, Lundeen & colleagues used weak measurement to map both imaginary and real components of a wavefunction directly, without destroying the state. It says: “with weak measurements, it’s possible to learn something about the wavefunction without completely destroying it”. And...

Hello, guys! I have a question. How can I prove the behavior of a particle subjected to an infinite potential? Will the wave function exist?

Where did they get the equation in circled in red from? It does not seem that it can be derived from the graph below. Many thanks

I see this written or talked about so often. Pop-sci for sure. But, whatever the wave function is, and whatever might collapse it, can we agree consciousness is not required to collapse it? I.E., the moon was there before "conscious" beings, on this planet or elsewhere, viewed it? Is at...

Why on Earth does anyone, let along Roger Penrose, think gravity might be what causes the wave function to collapse? The most basic experiment in quantum physics, the double slit experiment, shows that collapse is most closely analogous to whether or not the item at issue (for example, an...

Hi, I have hard time to really understand what's a stationary state for a wave function. I know in a stationary state all observables are independent of time, but is the energy fix? Is the particle has some momentum? If a wave function oscillates between multiple energies does it means that the...

Greetings, is it possible to characterize a sinusoidal wave in the domain of time and then pass into the domain of movement along x direction? I start with: a is the amplitude of the sine function and ω is the angular velocity. t is the time. I can express the angular velocity in funct. of the...

The known expression of the wave function is where A is the amplitude, k the wave number and ω the angular velocity. The mathematical definition of arc length for a generical function in an interval [a,b] is where, in our sinusoidal case: For our purpose (calculation of the length in one...

The textbook I am self studying says that the wave function for a free particle with a known momentum, on the x axis, can be given as Asin(kx) and that the particle has an equal probability of being at any point along the x axis. I understand the square of the wave function to be the probability...

The following is the wave equation from Electrodynamics: $$\frac{\partial^2 \Psi}{\partial t^2} = c^2\frac{\partial^2 \Psi}{\partial x^2}$$ Where ##\Psi## is the wave function. But because of Heisenberg's Uncertainty, physicists had to come up with another equation (the Schrodinger equation)...

How do spinors affect wave function solutions? Like how is the output different

So what am I doing wrong here? I can clearly observe it, I'm nearly sure I can tell which particles are going throw each slit if I used another laser too. My suspicion is that the electrical current of the photon detector that uses germanium or silicon to detect the particles are influencing the...

Is there a general expression for the wave function $\psi$, which describes the electronic properties of an arbitrary covalent bond? For example is it equal to some sort of trigonometric expression?

hi guys I am recently taking a Nuclear structure course, and have a lot of questions regarding the nuclear rotor model. in most nuclear physics books the I have, the wave function associated with the rotor model of the nucleus is written in terms of the Wigner D functions , like the expression...

Given a wavefunction ψ(x, 0) of a free particle at initial time t=0, I need to write the general expression of the function at time t. I used a Fourier transform of ψ(x, t) in terms of ψ(p, t), but, i don't understand how to use green's functions and the time dependent schrodinger equation to...

It is asking to derive the time-independent wave function and has managed to get the answer of and i am very confused as where (ix/a) and (-x^2/2a) came from ? Thanks.

I am totally confused about the task. Any help will be nice. Thank you so much

I was wondering, if we have a measurement of, say, spin of an electron, which can yield spin-up and spin-down in the context of MWI, then the electron gets entangled with the measurement device, yielding the wave function ##|Measurement_{spin-up}, Value_{spin-up} \rangle +...

I'm trying to find the wavelength. However, I don't understand why the wavelength is different if the wave is moving in the +z direction. I have ##\Psi(z=15cm,t) = \hat{x} 6 cos (\frac{\pi}{3}t)## ##\Psi(z=12cm,t + 2s) = \Psi(z=18cm,t)## For a wave moving on the -z direction I know that the...

The final wave function solutions for a particle trapped in an infinite square well is written as: $$\Psi(x,t) = \Sigma_{n=1}^{\infty} C_n\sqrt{\frac{2}{L_x}}sin(\frac{n\pi}{L_x}x)e^{-\frac{in^2{\pi}^2\hbar t}{2m{L_x}^2}}$$ The square of the coefficient ##C_n## i.e. ##{|C_n|}^2## is...

I first Normalise the wavefunction: $$ \Psi_N = A*\Psi, \textrm{ where } A = (\frac{1}{\sum {|a_n^{'}|^{2}}})^{1/2} $$ $$ \Psi_N = \frac{2}{7}\phi_1^Q+\frac{3}{7}\phi_2^Q+\frac{6}{7}\phi_3^Q $$ The Eigenstate Equation is: $$\hat{Q}\phi_n=q_n\phi_n$$ The eigenvalues are the set of possible...

Summary:: We are currently studying basics of quantum mechanics. I'm getting the theory part but it's hard to visualise everything and understand. We are given this question to plot the function so if someone could help me in this. Plot the following function and the corresponding g²(x) g(x)...

If ##\hat{T} = -\frac{\hbar}{2m}\frac{\mathrm{d^2} }{\mathrm{d} x^2}##, then the expectation value of the kinetic energy should be given as: $$\begin{align*} \left \langle T \right \rangle &= \int_{0}^{L} \sqrt{\frac{2}{L}} \sin{\left(\frac{\pi x}{L}\right)}...

Hi, I am 16 year old and I am very interested in Physics. This summer I solved Schrödinger equation using griffiths' introduction to quantum physics and other sources. I achieved to get an exact solution of the wave function but I would like to plot it in a programm in order to get the 3d...

Hello! Let's say we have a wave function. Maybe it's in a potential well, maybe not, I think it's arbitrary here. This wave function is one-dimensional for now to keep things simple. Then, we use a device, maybe a photon emitter and detector system where the photon crosses paths with the wave...

I started out by finding the w (omega) value for all of the three states but I'm not sure where to go from there.