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.
0
votes
1answer
32 views
What does the wavevector $\textbf{k}$ mean?
In Ashcroft, Mermin Solid State Physics, Eq. 17.43 is
$$
\epsilon(\textbf{k}) = \frac{\hbar^2 k^2}{2m} - e\phi(\textbf{r})
$$
where $\textbf{k}$ is the wavevector and all other symbols have their ...
2
votes
2answers
68 views
Interpretation of de Broglie wave
Until what point can the de Broglie wave be thought as a real wave?
I mean, is it made of something?
What amplitude does it have? Is it a sine wave?
How can it be related to the wavefunction of the ...
-1
votes
0answers
29 views
What values should the solved time-independent Schrodinger equation return? [closed]
I'm doing a project on Schrodinger's equation for my differential equations class. We solved the time independent function, and now we want to provide some examples of applying the equation by solving ...
1
vote
2answers
90 views
Can we measure “wavefunction” of quantum particles?
We know that there is uncertainty principle, so question: can we ever measure wavefunction of particles? I do not think this is possible, but I am not sure. I guess that everything is probabilistic. ...
0
votes
1answer
61 views
Periodic boundary condition on a Wave Function of a Particle in a Box
Until now solving the Schrodinger Equation for a particle in a box was relatively easy because the boundaries conditions imposed zero value on the wave function at the boundaries. But now I must find ...
1
vote
2answers
44 views
Time evolution of Gaussian wave packet
I'm slightly confused as to answer this question, someone please help:
Consider a free particle in one dimension, described by the initial wave function
$$\psi(x,0) = ...
0
votes
2answers
55 views
Electron in an infinite potential well
Does this problem have any sense?
Suppose an electron in an infinite well of length $0.5nm$. The state of the system is the superposition of the ground state and the first excited state. Find the ...
2
votes
0answers
59 views
A general wavefunction in a square lattice
Suppose we have a square lattice with periodic condition in both $x$ and $y$ direction with four atoms per unit cell, the configuration of the four atoms has $C_4$ symmetry. What will be a general ...
3
votes
1answer
33 views
Connection between a simple matter wave and Heisenberg's uncertainty relation
When looking at the wave function of a particle, I usually prefer to write
$$
\Psi(x,t) = A \exp(i(kx - \omega t))
$$
since it reminds me of classical waves for which I have an intuition ($k$ ...
2
votes
1answer
42 views
Hydrogen wave function in momentum space
We can seperate the wave function of an hydrogen atom in a radial and an angle part:
$$
\phi_{n,l,m} (\mathbf{r}) = R_{n,l,m}(r) Y_{l,m}(\vartheta,\varphi) \, ,
$$
where $Y_{l,m}$ are the spherical ...
0
votes
1answer
41 views
Time Dependent HydroHow would I go about writing the time dependent wave function given the wavefunction at $t=0$? gen Wave Function
1) How vwoulHow would I go about writing the time dependent wave function given the wavefunction at $t=0$?
go about writing the time dependent wave function given the wavefunction at $t=0$?
...
1
vote
1answer
75 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 ...
1
vote
0answers
56 views
Double Slit Problem Involving Superposition of Wave Equation [closed]
Here's my question:
To be clear it's part (iv) that's unclear to me.
I can see that the important bit is that the exposure is over a LONG time. Hence, this must have some implication on the manner ...
0
votes
1answer
39 views
Nodes and Antinodes for standing wave
In the arrangement shown in the figure below, an object of mass m can
be hung from a string (linear mass density $\mu$ = 2.00 g/m) that passes over
a light (massless) pulley. The string is connected ...
2
votes
2answers
122 views
Vector representation of wavefunction in quantum mechanics?
I am new to quantum mechanics, and I just studied some parts of "wave mechanics" version of quantum mechanics. But I heard that wavefunction can be represented as vector in Hilbert space. In my eye, ...
1
vote
1answer
73 views
Why does a plane wave have definite momentum?
Apologies if this is a little vague. It might not have a good answer.
Given the interpretation of $|\psi(x)|^2$ as a probability distribution it's unsurprising that a wave function that is ...
0
votes
1answer
97 views
Potential step and its transmission / reflection
Lets say we have a potential step with regions 1 with zero potential $W_p\!=\!0$ (this is a free particle) and region 2 with potential $W_p$. Wave functions in this case are:
\begin{align}
...
0
votes
1answer
105 views
How does one find the wave velocity and the phase speed?
While I was studying beats, I tried to find a displacement function of any particle in the most generalized form. I ended up with $$y=2A\sin(\pi(t-x/v)(f_1+f_2))\cos(\pi(t-x/v)(f_1-f_2)).$$
Now, ...
2
votes
2answers
94 views
Why the hydrogen radial wave function is real?
Why the hydrogen radial wave function is real?
Is it a coincidence?
0
votes
1answer
57 views
Why do people say the phase oscillates in time and the amplitude stays the same but the intensity of a traveling beam does oscillate with time?
I'm confused why people say the phase oscillates in time and the amplitude stays the same (the reason for having complex numbers). But on the other hand, the intensity of a traveling beam does ...
1
vote
2answers
88 views
Why does the wave description say that probability oscillates, while the phase interpretation says constant amplitude?
The wave description of a particle illustrates an oscillating probability of the particle being found in any point in space.
When a particle travels, it carries along with it a phase that oscillates ...
1
vote
1answer
81 views
normalizing a wavefunction
I have a homework problem that I can't get started on, below is the first bit. I feel like I should just be able to integrate to find $C$ but I get a divergent integral. Can someone give me a hint as ...
2
votes
1answer
60 views
Does the observer or the camera collapse the wave function in the double slit experiment?
Ok so if we setup a camera before the slit we will find a single photon and will follow through accordingly, likewise by having a camera setup after the slit, we can retroactivly collapse the wave ...
1
vote
0answers
26 views
Is there anything to prevent paired-up neutrons from a complete overlap
The reason "neutrons don't overlap", as DarenW explained it, has to do with intricate forces at play that take into account the spins, iso-spins and symmetry of the wavefunctions.
However, assume I ...
1
vote
1answer
37 views
Why is the Horizontal Force Constant in Deriving the One Dimensional Wave Equation
My textbook in deriving the wave equation for a one dimensional elastic string stated that the horizontal direction force is constant.I understand that the horizontal components of the tensions on ...
1
vote
1answer
146 views
Finite, square, potential well
Lets say we have a finite square well symetric around $y$ axis (picture below).
I know how and why general solutions to the second order ODE (stationary Schrödinger equation) are as follows for ...
0
votes
0answers
92 views
Scattering and partial wave analysis for cross section [closed]
Problem
Given the central potential:
$V(r)=-\frac{\hbar^2}{m a^2}\frac{1}{\cosh({r\over a})}$
and given that we know the solution to the following ODE
$\frac{d^2 y}{dx^2}+k^2 ...
-1
votes
1answer
88 views
Is normalization consistent with Schrodinger's Equation?
Schrodinger's Equation does not set a limit on the size of wave functions but to normalize a wave function a limit must be set. How is this consistent physically and mathematically with Schrodinger's ...
1
vote
1answer
49 views
Question about the linearity of wave functions
For piece-wise constant potential, the potential energy is constant so the time dependent wave function can take the form $\psi(x,t)=C_1e^{i(kx- \omega t)}+C_2e^{i(-kx-\omega t)}$ where ...
1
vote
1answer
71 views
Where is a particle bound in a delta potential?
I can picture a bound state in a harmonic oscillator, or in an infinite square well, but where is a particle bound in a delta potential?
1
vote
2answers
61 views
Wavefunction restrictions of odd potentials
So I was just reading back through Griffiths' "Introduction to Quantum Mechanics" and solving some of the problems for practice. There is a nice one (problem 2.1c for those playing at home) where you ...
1
vote
1answer
172 views
What does it mean for something to be a ket?
Ok so I will provide the following example, which I am choosing at random from Sabio et al(2010):
$$\psi(r,\phi)~=~\left[
\begin{array}{c}
A_1r\sin(\theta-\phi)\\
...
1
vote
1answer
270 views
Wave function and Dirac bra-ket notation
Would anyone be able to explain the difference, technically, between wave function notation for quantum systems e.g. $\psi=\psi(x)$ and Dirac bra-ket vector notation?
How do you get from one to the ...
1
vote
1answer
122 views
Cylindrical wave
I know that a wave dependent of the radius (cylindrical symmetry), has a good a approximations as $$u(r,t)=\frac{a}{\sqrt{r}}[f(x-vt)+f(x+vt)]$$ when $r$ is big. I would like to know how to deduce ...
0
votes
1answer
147 views
What does the wavefunction of atom look like at low temperature?
I am reading an introduction material on Bose-Einstein condensation (BEC) at low temperature and it stated that when the temperature approaches zero kelvin, almost all atoms are degenerated into the ...
0
votes
1answer
345 views
Gaussian wave packet
At our QM intro our professor said that we derive uncertainty principle using the integral of plane waves $\psi = \psi_0(k) e^{i(kx - \omega t)}$ over wave numbers $k$. We do it at $t=0$ hence $\psi = ...
1
vote
1answer
130 views
Once I have the eigenvalues and the eigenvectors, how do I find the eigenfunctions?
I am using Mathematica to construct a matrix for the Hamiltonian of some system. I have built this matrix already, and I have found the eigenvalues and the eigenvectors, I am uncertain if what I did ...
2
votes
2answers
152 views
In Dirac notation, what do the subscripts represent? (Solution for particle in a box in mind)
So the set of solutions for the particle in a box is given by
$$\psi_n(x) = \sqrt{\frac{2}{L}}\sin(\frac{n\pi x}{L}).$$
In Dirac notation $<\psi_i|\psi_j>=\delta_{ij}$ assuming $|\psi_i>$ ...
2
votes
1answer
56 views
In the expansion of the scattered wave function, why do these two functions have the same index?
See Griffiths Quantum Mechanics, eq. 11.21. Evidently,
$$\psi(r,\theta,\phi)=Ae^{ikz}+A\sum\limits_{l,m}^{\infty}C_{l,m}h_{l}(kr)Y_{l}^{m}(\theta,\phi).$$
But I don't see why the $l$th Hankel function ...
1
vote
3answers
171 views
Could quantum mechanics work without the Born rule?
Slightly inspired by this question about the historical origins of the Born rule, I wondered whether quantum mechanics could still work without the Born rule. I realize it's one of the most ...
0
votes
3answers
221 views
Normalisation factor $\psi_0$ for wave function $\psi = \psi_0 \sin(kx-\omega t)$
I know that if I integrate probabilitlity $|\psi|^2$ over a whole volume $V$ I am supposed to get 1. This equation describes this.
$$\int \limits^{}_{V} \left|\psi \right|^2 \, \textrm{d} V = 1\\$$
...
0
votes
1answer
107 views
Young experiment: square of classical real wave function
I can't understand why the sum of two real waves result in a time dependent wave, but not so for the complex waves.
In details, I can't get this passage on p.38-39 in A.C. Phillips, Introduction to ...
0
votes
0answers
264 views
Expectation value of a Gaussian wave packet [closed]
How can I compute the expectation value $\langle x\rangle_t$ of a Gaussian wave packet $$\psi(x,t) = \int_{-\infty}^\infty \mathrm dp \, \hat\psi(p) \exp{\frac{-\mathrm i(px - E_p t)}{\hbar}}? $$
...
2
votes
3answers
302 views
Confused over complex representation of the wave
My quantum mechanics textbook says that the following is a representation of a wave traveling in the +$x$ direction:$$\Psi(x,t)=Ae^{i\left(kx-\omega t\right)}\tag1$$
I'm having trouble visualizing ...
4
votes
2answers
322 views
Amplitude of Probability amplitude. Which one is it?
QM begins with a Born's rule which states that probability $P$ is equal to a modulus square of probability amplitude $\psi$:
$$P = \left|\psi\right|^2.$$
If I write down a wave function like this ...
1
vote
0answers
174 views
Probability and probability amplitude
What made scientists believe that we should calculate probability $P$ as the $P = \left|\psi\right|^2$ in quantum mechanics? Was it the double slit experiment? How? Is there anywhere in the ...
0
votes
1answer
381 views
Solving the time independent Schrodinger equation: Does a complex solution make sense?
In my notes, I have the Time Independent Schrodinger equation for a free particle
$$\frac{\partial^2 \psi}{\partial x^2}+\frac{p^2}{\hbar^2}\psi=0\tag1$$
The solution to this is given, in my notes, ...
7
votes
2answers
227 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 ...
3
votes
1answer
309 views
Expectation values-Wavefunction
I'm a bit puzzled about an excercise in which I have to find the expectation values for position and momentum. Normally this should be pretty easy but in this case I just don't get the point.
...
5
votes
3answers
364 views
Meaning of $\int \phi^\dagger \hat A \psi \:\mathrm dx$
While analysing a problem in quantum Mechanics, I realized that I don't fully understand the physical meanings of certain integrals. I have been interpreting:
$\int \phi^\dagger \hat A \psi ...
