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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759 views

Degeneracy in one dimension

I'm reading this wikipedia article and I'm trying to understand the proof under "Degeneracy in One Dimension". Here's what it says: Considering a one-dimensional quantum system in a potential ...
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1answer
38 views

Mathematical definition of wavefront in case of non harmonic waves

What is the general mathematical definition of wavefront? Wavefront is the surface where, at fixed time, the phase is constant But for non-harmonic waves we cannot talk about phase as the ...
4
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1answer
76 views

Dirac Equation in RQM (as opposed to QFT) is written in which representation?

In introductory Quantum Mechanics treatments it is common to see the Schrödinger's equation being written, simply as: ...
3
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5answers
177 views

Where does $\hat{P}\psi(x) = -i\hbar \partial_x \psi(x)$ come from?

It's a very basic question, where does the relation $$\hat{P}\psi(x) = -i\hbar \partial_x \psi(x)$$ for any square integrable $\psi(x)$ come into existence? Some texts I found states that the above ...
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1answer
74 views

Eigenstates of position and momentum operators in QM

In Griffiths pages 103-105 "Introduction to Quantum Mechanics" 2nd editiion he states that the eigenfunctions of the position and momentum operators are $$g_y(x) = \delta(x-y)$$ where the eigenvalue ...
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3answers
526 views

Quantum Mechanics in Electric Field

I am working on a problem which looks like this. Consider a charged particle with charge $q$ trapped in a box of length $L$ with finite constant potential $ V_0 $ on both ends. A constant (static) ...
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4answers
2k views

What is a wave function in simple language?

In my textbook it is given that 'The wave function describes the position and state of the electron and its square gives the probability density of electrons.' Can someone give me a very ...
3
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2answers
87 views

What happens when two wavefunctions meet?

Apologies for the over-broad question(s), but I'm having a hard time finding out where to look to answer these myself: If a particle is a wavefunction describing a probability amplitude distributed ...
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0answers
92 views

Modern interpretation of wave-particle duality

As far as I understand, in the early days of quantum theory there was quite a lot of debate over how to interpret what it meant for a quantum mechanical object to exhibit both wave-like and ...
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1answer
41 views

Infinite depth potential well (energy probability) [on hold]

Consider a particle in an infinite depth potential well of length 2a. The particle is in a state in which it is described by the wavefunction $\psi (x)=A(a^2-x^2)$ for $-a\leq x \leq a$ with a ...
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1answer
136 views

About 'de Broglie hypothesis' and the double slit experiment

EDIT: As i mentioned in my original question, i do not have the background to fully understand @Timaeus answer (which was very detailed indeed). I would appreciate if someone could give a more ...
0
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0answers
11 views

Using Desmos to trace function fields [closed]

Using the online tool of creation of graphic desmos, is there any way to plot a graph 3D in function of their electric field and magnetic field? like that: I'm trying to use the following ...
-1
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2answers
73 views

Does uncertainty exist without consciousness? [closed]

How can uncertainty exist without conscious beings calling something uncertain? When you look at the uncertainty principle, it only makes sense if consciousness collapses, disturbs, interfere's with ...
10
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1answer
150 views

What is known about the hydrogen atom in $d$ spatial dimensions?

In a first (or second) course on quantum mechanics, everyone learns how to solve the time-independent Schrödinger equation for the energy eigenstates of the hydrogen atom: $$ ...
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2answers
1k views

Mathematical explanation of quantum teleportation

I am now studying quantum teleportation. I get what the process is like but I'm wondering why it happens this way. You've got two entangled particles A and B whose wavefunctions are entangled. You ...
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1answer
73 views

Propagating a Gaussian wavepacket backwards in time

So, I'm following the MIT OCW lectures on 8.04 quantum mechanics by Prof. Allan Adams. I have the expression for the probability distribution of a gaussian wavepacket for a free particle situation. No ...
3
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1answer
42 views

Behavior of atom's wave packets in a gas

It is my understanding that the wave packet of a free localized particle spreads with time. My question is what is the best description of the particles in a gas inside a closed container: Do they ...
8
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4answers
424 views

Is it possible for $\Delta x$ ($\sigma_x$) of any free particle wave packet to be decreasing at any time?

Consider any wave packet describing a free particle (so no potential or other forces acting on it). Then it can be shown that $\Delta p$ does not change in time. However, my question is what happens ...
35
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6answers
3k views

Does Heisenberg's uncertainty under time evolution always grow?

Recently there have been some interesting questions on standard QM and especially on uncertainty principle and I enjoyed reviewing these basic concepts. And I came to realize I have an interesting ...
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votes
2answers
49 views

What makes the probability distribution of a wavefunction in QM intrinsic? [closed]

I know that the usual interpretation of the wavefunction in QM is that it´s associated with a probability distribution of measurable quantities. Not a deterministic probability (like the probabilities ...
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0answers
20 views

Overtone Transition Probability

For an anharmonic potential, like the morse potential, higher order transitions (overtone) with $\Delta n=\pm2,\pm3,..$ are allowed. How do I calculate the probability $P$ for such transitions? My ...
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1answer
37 views

Rate of the increase of width of a Gaussian wavepacket

So, I'm following the MIT OCW lectures on 8.04 quantum mechanics by Prof. Allan Adams. I have the expression for the probability distribution of a gaussian wavepacket for a free particle situation. No ...
11
votes
0answers
144 views

What's the lowest nuclear charge $Z < 1$ that will support a bound two-electron ion $(Z,2e^-)$?

In my programming project I calculate the minimal energy of an atom with 2 electrons in the $L=0, S=0$ state, using a Hylleraas wave function. The values I find for $Z=2$ (He) and $Z=1$ (H$^-$) are ...
0
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1answer
190 views

Probability and double slit

if a beam of identical particles at random distances from each other (or exactly 1/2 lambda between each other) travelling with the same v towards a double sllit do not interfere with each others wave ...
9
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1answer
621 views

Non-separable solutions of the Schroedinger equation

I'm studying an undergraduate Quantum Mechanics course and I have some doubts about the solution of the Schroedinger equation by the separation of variables method. If we suppose that the solutions ...
4
votes
3answers
1k views

Born Interpretation of Wave Function

I have just started Griffiths Intro to QM. I was studying Born's interpretation of Wave function and it says that the square of the modulus of the wave function is a measure of the probability of ...
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0answers
64 views

Usage of Complex Numbers in Quantum Mechanics [duplicate]

In Griffiths 2nd Edition Quantum Mechanics page 148, it says when describing the eigenfunction to a part of the central potential problem as $$\mathrm e^{i m \phi}$$ "In electrodynamics we would ...
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2answers
149 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?
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0answers
55 views

Finding $\psi(0)$ using Schrodinger equation with potential $U(x) = q\delta(x)$

I am having some trouble answering the following question in my "Advanced Quantum Mechanics" course: Using the integral equation: $$\psi(x) = Ae^{ikx} + Be^{-ikx} - ...
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1answer
53 views

Interpreting group velocity of free particle wave packet

I am trying to understand the concept of group velocity of a free particle wave packet: $$\Psi(x,t) = \frac{1}{\sqrt{2 \pi}}\int_{-\infty}^{\infty} \phi(k)e^{ikx}e^{-\frac{i \hbar k^2 t}{2m}}dk.$$ ...
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0answers
16 views

3d wave packet form of a free particle

Consider the 3d wave packet of a free particle moving along the x-axis. The wave packet will have components in the y and z dimensions as well as the x dimension. What form do they take? Are they ...
0
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1answer
267 views

Semi-infinite / Asymmetric potential well

I'm asked to come up with an ansatz and solve for the coefficients of a asymmetric infinite potential well, where: $$ V = \begin{cases} \infty \text{ for } x< 0 \\ V_0 \text{ for } 0 \leq x \leq L ...
3
votes
2answers
2k views

Coupled quantum harmonic oscillator

Given the following Hamiltonian for two identical linear oscillators with spring constant $k$ and interaction potential $\alpha x_1x_2$; I was asked to find the expectation value $\langle ...
3
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1answer
639 views

Density of classical states in quantum theory

Let's first treat electrons as classical objects. I can evaluate the classical energy of each state in a configurational space (3N real numbers and, say, spins) using just Coulomb's law. Then I ...
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1answer
35 views

What processes create or destroy information?

From a classical standpoint, it seems pretty clear that information can be easily lost. If you knock over a bookshelf and the books fall out, it seems like their initial order on the shelf cannot be ...
0
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1answer
158 views

How can energy be negative in a finite square well?

Say if the potential $V(x) < 0$ in the well but the sides or the scattered states its zero potential, anyways How is that the energy in the well is less than zero? Is it because the potential ...
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0answers
20 views

Solving traveling wave using the shooting method

The spatially-dependent Hodgkin-Huxley equation for a cylindrical dendrite or unmyelinated axon: where $\frac{a}{2\rho}\frac{\partial^2V}{\partial x^2}$ is a diffusion term $a$ is the fiber radius, ...
0
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1answer
17 views

Connection between singlet, triplet two-electron states and the Slater determinant

I'm confused about a number of things concerning two-electron systems and spin. Here is (perhaps too much) exposition, skip to "the problem" if you want: Consider the helium atom in the simplified ...
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0answers
59 views

How did Max Born come up with his rule? [duplicate]

In his rule, he stated that the probability is norm-squared of wave function, $|\psi|^2$. And as far as I knew, no one else at that time had "right" interpretation of the wave function. Even ...
1
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1answer
51 views

Can particle quantum spin be described with a wave function? [closed]

I'm a little confused about the idea of spin. It's been non-technically described to me as "like magnetic dipole moment", except only two possible "directions". But I feel like that's a bad analogy, ...
-3
votes
2answers
87 views

Is the Wave Function a Unitary Operator? [closed]

A unitary operator can be represented as an exponential $$e^{iA}$$ and as we represent the wave function in general as $$e^{i k x}.$$ Does that mean that the wavefunction is unitary as the exponent is ...
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0answers
26 views

Parts of the Quark Wavefunction

Quarks are fermions meaning that they have an antisymmetric wavefunction. Under particle exchange the sign of the wavefunction. The wavefunction is made up of a few different parts $$ \psi_{Total} = ...
4
votes
2answers
106 views

Where the time-dependent wavefunction $\Psi(\vec{x},t)$ lies?

Supose $\vec{x}=(x,y,z)\in \mathbb{R}^3$. The state of a physical system is described by the function $\Psi(\vec{x},t)$, where it must satisfy $$\int_{\mathbb{R}^3} ...
0
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2answers
56 views

Confusion of Schrödinger equation and complex conjugates

I have a similar question that was asked in the following link: (Schrödinger's Equation and its complex conjugate). But I find both the question and answers not specific enough. So let me ...
0
votes
2answers
59 views

Linear Combinations of Energy Eigenfunctions in 1D

Given that a particle is in a state defined by the wavefunction: $$\Psi (x,t) = \psi_0(x)e^{-iE_0t/\hbar}+\psi_1(x)e^{-iE_1t/\hbar}$$ where $\psi_0(x)$ and $\psi_1(x)$ are the energy eigenfunctions of ...
2
votes
1answer
46 views

Wavefunction Collapse

I believe my Lecturer and the textbook have contradicted one another. My lecturer gave the example that if the spatial part of the wavefunction of a particle is given by $\psi(x) = c_1\psi_1(x) + ...
1
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1answer
41 views

1D Scattering Phase Shift (Finite Well) - Unphysical?

I am calculating the phase shift from a 1-dimensional potential well. This seems extremely simple, but I am just getting so confused by it. Let there be a potential well of depth $V_0$ and spatial ...
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1answer
27 views

Taking Measurements of Quantities in QM

I have a quick question relating to Annihilation and Creation operators, and in taking observables in general. Let's say, for instance, that I prepare a particle so that I consider the projection of ...
0
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2answers
56 views

What do operations on single Qubits of Unfactorable Superpositions Do?

So suppose I have the following Quantum Circuit: A ---- |Control| -----|Hadamard|---- B ---- |xxxxxxx|------------------------ Which is a 2 input Controlled Gate (applying some gate of two choices ...
0
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2answers
3k views

Schrödinger's Equation and its complex conjugate

I would like to know why there is a minus sign on the right-hand side of the Schrödinger's complex conjugate equation, whereas in the Schrödinger's equation there isn't. I know it is a simple ...