A complex scalar field that describes a quantum mechanical system. The square of the modulus of the wave function gives the probability of the system to be found in a particular state.

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Transition from coordinate space to momentum space for SHO

I am given that the ground state of the SHO in position space is given as $$\langle q|\psi_0\rangle=\frac{1}{a^{\frac12}\pi^{\frac14}}e^{-q/4a^2}$$ Where a is a constant with units of length. I am ...
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90 views

Particle in a higher-dimensional box with an attractive delta potential

Suppose you have a particle in the box $[0,L]^d$, with an attractive Dirac delta potential $-\delta_{\vec w}(x)$ at $\vec w$. How do you solve the Schroedinger equation for this system? In the case ...
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1answer
72 views

Does light or observation collapse wave functions? [duplicate]

I hear that observation is what causes the wave function collapse, but that doesn't make sense considering that an eye or camera is just a physical system with no particularly special properties. In ...
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103 views

Superposition and density matrix. What are these states?

I just wanted to understand the following. Let's stay with the harmonic oscillator in QM, just to have an example at hand. First, there are all the different states for $n=1,2,...$. (Let's call them ...
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55 views

QM 2D Gaussian wave packet translation

I've been reading a lot but cannot find an example of 2D Gaussian wave packet moving in a particular direction. I've done some of the math myself, in a 1D case, and then kind of guessed the ...
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1answer
716 views

Simple Quantum Mechanics question about the Free particle, (part1)

I am reading Introduction to Quantum Mechanics by David Griffiths and I am in Ch2 page 59. He starts out writing the time dependent Schrödinger equation and the solution for $\psi(x,t)$ for the free ...
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1answer
67 views

Question on measuring expectation value of spin with time variation

I have a particle with the following wave function: $$\psi(t) = \frac12 |\uparrow \rangle e^{-i(\omega_1+\omega_2)t/\hbar} +\frac12 |\uparrow \rangle e^{-i(\omega_1-\omega_2)t/\hbar} ...
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117 views

Basic introductory quantum mechanics question [closed]

Given that $\psi = \frac{1}{\sqrt{32 \pi a_{0}^{3}}}(2-\frac{r}{a_0})exp(\frac{-r}{2a_0})$ is a wavefunction of the hydrogen atom, write down the probability density for r and calculate the ratio ...
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1answer
118 views

Spin state of electron after measurement

I have a system of two spin 1/2 particles in a superposition of spin states in the z-direction given by: $\psi = \frac{1}{2} |+ +\rangle + \frac{1}{2} |+ -\rangle + \frac{1}{\sqrt{2}} |- -\rangle$ ...
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1answer
102 views

Quantum state with zero standard deviation of position operator

Is any quantum state $|\psi\rangle$ possible such that the standard deviation $\sqrt{\langle\psi|(\Delta\hat{x})^2|\psi\rangle}$ of the position operator $\hat{x}$ is zero? If not, why?
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138 views

Double slit experiment and entanglement

Just wondering, what would happen in this experiment. In the experiment you would first have two entangled particles. Then you fire one of the particles, lets say "Particle A", at a double slit ...
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35 views

Rydberg quasimolecules & stark states?

I found this image : on the internet and I traced it back to this article ,I wanted to use it as part of an architectural visualization for my project(architecture) but for this to happen I need to ...
4
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1answer
168 views

Virial theorem and variational method: an exercise (re-edited)

I have a hydrogen atom, knowing that its Hamiltonian has been modified turning the standard potential $$ V_{0}(r) = -\frac{Z}{r} $$ into $$ V(r) = -\frac{g}{r^{\frac{3}{2}}} $$ with $g$ a positive ...
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1answer
91 views

Angular momentum of hydrogen from $n,l,m$ values

Given a wavefunction for hydrogen $\psi(n,l,m)$ it is possible to calculate its associated energy from $E=-13.6/n^2$. Does a similar equation exist for $L^2$ and $L_z$? That is, if we are given the ...
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0answers
92 views

Functionals of quantum states in QFT

Almost every book and article I can think of represents states of QFT using the Heisenberg picture of Hilbert space vectors, but Visser in "Lorentzian wormholes" does mention that you can also ...
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1answer
142 views

Infinite potential square well solutions

My question is about understanding the different solutions of the potential square well. Imagine a square well defined this way: $$ V(x) = \begin{cases} ∞&\,{\rm if} x<0 \\ 0&\,{\rm ...
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1answer
144 views

Spin eigenvalues and eigenvectors problem. Is this the correct way to solve it?

An electron is described by the Hamiltonian $ H=\frac{e}{mc}\bar{S}\cdot\bar{B} $ where $\bar{S} =(S_x,S_y,S_z)$ is the spin operator and $\bar{B}$ the magnetic field. For $t>0$ ...
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450 views

Does the wave function always asymptotically approach zero?

I'm new to quantum physics (and to this site), so please bear with me. I know that quantum mechanics allows particles to appear in regions that are classically forbidden; for example, an electron ...
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3answers
85 views

At what point is the spin determined in a Stern-Gerlach Apparatus

Consider a particle with spin that travels through a Stern Gerlach box (SGB), which projects the particle’s spin onto one of the eigenstates in the $z$-direction. The SGB defines separate trajectories ...
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1answer
180 views

Energy and time evolution of a particle in a potential well

Hoping this is not a silly and stupid question let me ask for help in this problem. I have a particle in an infinite square well (the box is from 0 to a), in the state described by the function ...
5
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2answers
123 views

Inexact measurement and wavefunction collapse

As is usually said, measurement of an observable $q$ leads to collapse of wavefunction to an eigenstate of the corresponding operator $\hat q$. That is, now the wavefunction in $q$ representation is ...
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3answers
544 views

Superconducting Wavefunction Phase (Feynman Lectures)

In Volume 3, Section 21-5 of the Feynman lectures (superconductivity), Feynman makes a step that I can't quite follow. To start, he writes the wavefunction of the ground state in the following form ...
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5answers
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Example of the time-independent Schrödinger equation having a complex solution?

We know $\Psi(x,t)$ is complex, but can $\Psi(x)$ be complex? I have seen particle in a box, well and harmonic oscillator. All have real solutions for time-independent Schrödinger equation. Hence, I ...
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4answers
340 views

Can we safely assume $\Psi(x,t) = \psi(x)e^{-i\omega t}$ always in QM?

In the particle in a box, harmonic oscillator and in Hydrogen Atom, we can safely assume $$\Psi(x,t) = \psi(x)e^{-i\omega t}.$$ So why not make it a postulate to consider the wave function to be ...
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65 views

Quantum eraser double slit experiment

In the quantum eraser double slit experiment, does the photon (or wavefunction) pass through one slit or both slits when different polarizers are placed over the slits?
7
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254 views

Virial theorem and variational method: a question

I have an hydrogenic atom, knowing that its ground-state wavefunction has the standard form $$ \psi = A e^{-\beta r} $$ with $A = \frac{\beta^3}{\pi}$, I have to find the best value for $\beta$ ...
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566 views

Particle in a 1-D box and the correspondence principle

Consider the particle in a 1-d box, we know very well the solutions of it. I'd like to see how the correspondence principle will work out in this case, if we consider position probability density ...
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3answers
408 views

Comparison of 1D and 3D wave functions

When discussing the Schroedinger equation in spherical coordinates, it is standard practice in QM handbooks to point out that the radial part of the 3-dimensional wave equation bears a strong analogy ...
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208 views

How axiomatic is the symmetrization requirement (i.e. the Pauli principle)? (in QM)

I've so far always been told, that the symmetrization requirement is an axiom on the level of the Schrödinger equation and the statistical interpretation of the wave function (or it's absolute value). ...
3
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2answers
174 views

Why does $\ell=0$ correspond to spherically symmetric solutions for the spherical harmonics?

In quantum mechanics why do states with $\ell=0$ in the Hydrogen atom correspond to spherically symmetric spherical harmonics?
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262 views

A difference between Plane Wave and Collimated?

Collimation is clearly in reference to ray($\vec{k}_{xy}$ vector) orientation unlike waterfront continuity( $\phi_{xy}$ phase shift) described by plane-wave. Not to say that one is not directly ...
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428 views

Is the wave function of a particle re-created after a measurement stops?

Yeah, I haven't quite understood, or been told, what happens to, for example an electron and it's wavefunction, when you stop to measure it? I mean, an electron has a wave function describing it's ...
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1answer
75 views

Can the wavefunction of a system be reconstructed from density matrices of subsystems?

Suppose we have several interacting particles in pure state $\left|\psi\right>$. For each of particles we can extract density matrices via $$\rho_i(x_i,x_i^\prime)=\int ...
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28 views

The influence of the expanding universe on the wave function

I was puzzled by a question on a physics fora about a possible connection between the expansion of the universe and the wave function. So, a photon's red shift tells us something about the expansion, ...
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2answers
243 views

General wavefunction and Schrödinger Equation

I'm starting with quantum mechanics and the book I follow (Griffiths) first introduces the wavefunction as the probability density of the position of a 0-spin single particle. Later on I've realized ...
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311 views

How can particles travel in a straight line?

A particle can be set off in a certain direction by giving them momentum. Momentum is a vector, so the particle heads off in a specific direction. But the wave function of the particle allows it to ...
4
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1answer
111 views

Can general wavefunctions be expressed as kets?

I am confused on bra-ket notation in quantum mechanics. My professor says that a ket is an eigenfunction of some operator. However, for some time now I thought a ket could represent a general ...
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1answer
140 views

Notation in Quantum Mechanics

When we write equations in QM, in certain places, the wave function is represented as $\psi(x,t)$, which is the wave function in position space, and in some other places, it is written as $\Psi(t)$. ...
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1answer
164 views

Probability in Quantum Mechanics: General

How do I find the most probable value of position of a (non-Gaussian) wave function? Is it the same value as the expectation value of the position? And is it true that the most probable value of ...
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2answers
178 views

Bloch wave function orthonormality?

there is this text book that is giving me a hard time for a while now: It shows that Bloch wave functions can be written as $$\Psi_{n\vec{k}}\left(\vec{r}\right) = \frac{1}{\sqrt{V}}e^{i\vec k \vec ...
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4answers
566 views

Is the wave function objective or subjective?

Here is a question I am curious about. Is the wave function objective or subjective, or is such a question meaningless? Conventionally, subjectivity is as follows: if a quantity is subjective then ...
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1answer
105 views

Product of position eigenvectors at different times

I've been thinking about this, and it might sound like a stupid question, but I can't seem to find an answer anywhere, here goes: Whenever we calculate expecation-values between two position ...
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1answer
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Ground State Wavefunction of Two Particles in a Harmonic Oscillator Potential

Question: Two identical, non-interacting spin-$1/2$ particles are in a 1D Harmonic Oscillator Potential. Their Hamiltonian is given by ...
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1answer
152 views

Phase shift in electromagnetic potential

In Aharonov-Bohm effect, how to derive that the wave function of a electric charge $q$ acquires a phase shift $\phi=\frac{q}{\hbar}\int \mathbf{A} \cdot d\mathbf{x}$ after travelling in the non-zero ...
5
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1answer
286 views

Boundary conditions from single-valuedness of spherical wavefunctions

This question is a follow-up to David Bar Moshe's answer to my earlier question on the Aharonov-Bohm effect and flux-quantization. What I forgot was that it is not the wavefunction that must be ...
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2answers
149 views

Does Schrödinger equation have dual-property with Heat equation?

I have experimental data that Schödinger equation maintains high frequencies, while heat equation low. Does Schrödinger equation have some duality property with heat equation?
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Which number should I suppose to $a$ (width of well) and $m$ (mass of particle) in potential well problem? [closed]

I tried to plot a complete of state functions of potential well problem but graph was so weird. I thought a cause was variables a and ...
2
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1answer
130 views

Possible Outcomes from Measuring a Hydrogen Atom

A hydrogen atom is characterized by the wavefunction $$\mid \psi \rangle =\sqrt{\frac{2}{7}}\mid 4\,2\,1\rangle +\sqrt{\frac{1}{7}}\mid 2 \,1\,\bar{1}\rangle+\sqrt{\frac{4}{7}}\mid 3\,2\,0\rangle$$ ...
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2answers
215 views

Area under the graph of squared wave function

I was given a graph of square of the wave function of a hydrogen atom, against the distance of the electron from the nucleus (denoted by r). What I know is that the square of the wave function gives ...
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1answer
138 views

Modulus Square of the Gaussian Wave Packet for uncertainty in $p$

Upon evaluating the integral (2.67) and obtaining the complex valued equation given in box 2.4, the author performs the modulus square to obtain the Gaussian distribution (2.68). How does one go about ...