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.

learn more… | top users | synonyms

-1
votes
2answers
92 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
votes
1answer
162 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: $$ \left(-\frac{\hbar^2}{2\...
3
votes
1answer
47 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 ...
0
votes
0answers
22 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 ...
0
votes
1answer
74 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 ...
0
votes
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 ...
-3
votes
2answers
54 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 ...
10
votes
2answers
640 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 ...
0
votes
0answers
66 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 ...
0
votes
0answers
58 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} - \int_{-\infty}^{\infty}G^{\pm}(...
0
votes
0answers
24 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
votes
1answer
57 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: $$\Psi(x,t) = \frac{1}{\sqrt{2 \pi}}\int_{-\infty}^{\infty} \phi(k)e^{ikx}e^{-\frac{i \hbar k^2 t}{2m}}dk.$$ ...
11
votes
0answers
153 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
votes
0answers
23 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, ...
1
vote
1answer
40 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
votes
1answer
26 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 ...
1
vote
0answers
64 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
vote
1answer
69 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, ...
1
vote
0answers
30 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} = \...
-3
votes
2answers
93 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 ...
0
votes
2answers
60 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 ...
2
votes
1answer
53 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) + c_2\...
1
vote
1answer
53 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 ...
1
vote
1answer
30 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
votes
0answers
32 views

Are $\psi ^{*}(x,t)$ and $\psi(x,-t)$ solutions of the same Schroedinger equation?

I have this question: Let $\psi(x,t)$ solution of the Schroedinger equation for a particle under a potential V(x) independent of time. Are $\psi ^{*}(x,t)$ and $\psi(x,-t)$ solutions of the same ...
0
votes
2answers
77 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 ...
7
votes
3answers
499 views

Interpretation of boundary conditions in time-independent Schrödinger equation

The time-independent Schrödinger equation: $$\ -\frac{\hbar^2}{2m}\frac{d^2\psi}{dx^2} + V\psi = E\psi$$ is second order, so we should expect the solution to have two "degrees of freedom" which can ...
11
votes
2answers
560 views

Tensor product in quantum mechanics?

I often see many-body systems in QM represented in terms of a tensor products of the individual wave functions. Like, given two wave functions with basis vectors $|A\rangle$ and $|B\rangle$, belonging ...
0
votes
1answer
48 views

Allowed Wave Functions of System

Given a single-particle system with Hamiltonian $H$, what constraints can be put on the wave function at a particular point in time $\psi(x)$? Of course $\psi(x)$ must obey boundary conditions given ...
0
votes
0answers
47 views

How to find the minimum value of potential in QM?

In MIT problem sets I followed a solution of an exercise which focuses on odd-parity energy eigenstates in finite square well. The point of problem is how to know or find the minimal value of ...
4
votes
3answers
112 views

Same quantum states represented in different basis

In literature on an introduction to quantum mechanics which I am working through, there is a section which explains that a vector has different representations based on the basis you choose and then ...
0
votes
1answer
27 views

Reflection in Finite Square Wells

For a Finite Square Well where we have a wavefunction $\psi(x)$ which is an energy eigenfunction with eigenvalue $E = 2V_0$ in the following potential: $V(x) = \begin{array}{ll} 6V_0 &...
0
votes
1answer
43 views

Wavefunction of a system of particles

A three-dimensional volume $V$ contains a certain number $N$ of electrons and they can't escape the volume $V$. Assume for simplicity that the potential $\mathcal{V}(\mathbf{r})$ is zero in all the ...
0
votes
2answers
65 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 ...
17
votes
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 ...
7
votes
3answers
219 views

What do the wave functions associated to the Fock states of each mode of a bound state system mean?

$\renewcommand{\ket}[1]{\left \lvert #1 \right \rangle}$ Consider a string of length $L$ under tension and clamped on each end. This system is described by the wave equation and has a set of modes. ...
2
votes
3answers
52 views

Position and momentum measurement effects on wave functions

I have a few short questions about an interpretation of what happens with position and momentum wave functions described in literature I am using. Given momentum space wave function and position space ...
0
votes
1answer
56 views

Can there be a wave function that is physically possible but is non differerentiable (maybe even non-continous)?

The definition of a wave function demands continuity and differentiability so that it can satisfy the Schrödinger Equation. My question is whether this assumption is necessary for reality. Does ...
0
votes
0answers
43 views

Singlet and triplet excited states in He atom

I found the following example for Term symbol usage in my coursebook: There are two electrons in He atom. Let the first one $e_{1}$ be in ground state, with $n_{1}=1$, $l_{1}=0$, $m_{l1}=0$, $m_{s1}...
0
votes
1answer
64 views

Would a collection of entangled particles behave like a superfluid? [closed]

Superfluidity of a Bose-Einstein condensate comes from the fact that all the particles are found in the same quantum state. They are described by the same macroscopic wavefunction. They never collide ...
1
vote
1answer
42 views

Correlating two definitions of bound states in quantum mechanics

In Griffiths, he defines a bound state to be that stationary state for which the total energy E is such that $E<V(\pm\infty)$. Let $\psi(x)$ is a stationary state satisfying $E<V(\pm\infty)$ and ...
1
vote
2answers
68 views

Observer in the double slit experiment with photons

In the double slit experiment with photons, the interacting observer is an instrument, detector… If you replace the detector with a piece of metal with the same mass as the mass of the detector, the ...
0
votes
1answer
102 views

Wave function of particle and antiparticle

The wave functions of particle and antiparticle are related by complex conjugation and wavefunction $Ψ$ must be complex for particle such as $n$, $p$. Is there way to prove this mathematically? Can we ...
0
votes
1answer
47 views

How to calculate probability of complex wave functions? [closed]

An election has an equation as such: $$Ψ(x) = e^{iαx^2}.$$ How am I supposed to find the probability of finding the electron over a certain range? Is Fourier Transform involved in this?
2
votes
1answer
91 views

Is there a way to prove that a bound state wavefunction can always be chosen real for an arbitrary potential in Quantum Mechanics?

As we can prove many things that always (at least in introductory quantum mechanical problems) apply using an arbitrary potential (like that $E>V_{\rm min}$ or else the solutions are non-...
3
votes
2answers
49 views

Quantum Mechanics: Can the probability of finding a particle in the whole space be smaller or higher at certain times?

In the book Introduction to Quantum Mechanics (by David Griffith) there is an Example 2.1: Suppose a particle starts out in a linear combination of just two stationary states: $$\Psi(x,0)~=~c_1\...
0
votes
1answer
22 views

Gauge transformation of wave function of a system of stationary charges

Let's say we have a system of $n$ stationary charges interacting via Coulomb potential. Let's ignore possible external electromagnetic fields. Moreover the system is quantum, and its wave function is $...
0
votes
0answers
49 views

Interpretation of a case of the double square well

Consider a 'double square well' potential (where $E < 0$) defined as: $$V(x) :=\begin{cases} -V_0~~~~~~~~~~~~~\text{for }\frac{b}{2} < x < \frac{b}{2} + a \text{ and } -a - \frac{b}{2} < ...
0
votes
0answers
20 views

wave propagation modelling

what is the best modelling technique for modelling mm-wave propagation in electromagnetic environment. Right now,am working on how to use use Transmission-line matrix (TLM) and ray-tracing techniques
2
votes
1answer
101 views

Particle here at a given time, in another galaxy a second later… Really?

I read "The Quantum Universe (Cox & Forshaw)" that a particle can be measured at a given position at a given time, and in another galaxy one second later. The probability of such event may be ...