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.
4
votes
1answer
205 views
Young's double slit
Am I right to think the (general) probability distribution of photon in a double slit experiment at the screen has the form $|\psi|^2 = c e^{\alpha x^2}\cos^2(\beta x)$? (Due to the superposition of ...
2
votes
1answer
264 views
Superposition of wavefunctions
Suppose you have 2 normalized wavefunctions $\psi_1=Ne^{iax}e^{if(x)}e^{i\omega t}$ and $\psi_2=Ne^{-iax}e^{if(x)}e^{i\omega t}$ defined on $x\in [-x_0,x_0]$ and vanishes for $|x|>x_0$. What then ...
2
votes
1answer
319 views
Simple rotation of an atomic orbital wavefunction
We know that an atomic orbital wavefunction may be written in terms of polar coordinates, $$\psi (r, \theta, \phi) = R(r) A(\theta, \phi)$$
where $R(r)$ is the radial component and $A(\theta, \phi)$ ...
2
votes
0answers
112 views
Spin 1/2 finite-difference field simulator?
Is there a finite-difference field simulator for spin 1/2 fields, something like meep for electromagnetism (spin 1)? Looking for something free (GNU, MIT or other open/free style license) and easy ...
4
votes
2answers
308 views
Exactly how is the constant measured velocity of light deduced from Maxwell's equation?
For electromagnetic radiation the velocity of propagation is $c = 1/\sqrt{\mu_0 \epsilon_0}$. Since both $\mu_0$ and $\epsilon_0$ do not vary in any inertial frame, then $c$ must be constant in any ...
1
vote
1answer
263 views
Sudden change in the Hamiltonian
Could someone explain what this sentence mean? "If the Hamiltonian changes suddenly by a finite amount, the wavefunction must change continuously in order that the time-dependent Schrodinger equation ...
3
votes
1answer
194 views
Projection of states after measurement
Continuing from the my previous 2-state system problem, I am told that the observable corresponding to the linear operator $\hat{L}$ is measured and we get the +1 state. Then it asks for the ...
0
votes
2answers
430 views
Plotting a wave function that represents a particle
The problem is this:
A particle is represented by the wave function $\psi = e^{-(x-x_{0})^2/2\alpha}\sin kx$. Plot the wave function $\psi$ and the probability distribution $|\psi(x)|^2$.
This ...
1
vote
2answers
224 views
Schematic expression of the Schrodinger equation
it would be great if someone could help me understand the following quote regarding wavefunctions :)
"$$\psi(x)=\sum_n C_nu_n(x)+\int dE C(E)u_E(x)$$ The expression is schematic because we have ...
1
vote
1answer
326 views
Determining wave function for term symbol 1D
I am trying to follow a book (Introduction to Ligand Field Theory by Ballhausen in 1962 on pg 15), but it isn't clear how they make a particular leap.
Background
I want to find the wave function for ...
3
votes
3answers
413 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 ...
3
votes
3answers
588 views
Historical background of wave function collapse
I wonder what were the main experiments that led people to develop the concept of wave function collapse? (I think I am correct in including the Born Rule within the general umbrella of the collapse ...
3
votes
1answer
677 views
Confusion between the de Broglie wavelength of a particle and wave packets
So I learned that the de Broglie wavelength of a particle, $\lambda = \frac{h}{p}$, where h is Planck's constant and p is the momentum of the particle. I also learned that a quantum mechanics ...
0
votes
1answer
165 views
Help me to visualize this wave equation in time, to which direction it moves?
The wave is
$\bar{E} = E_{0} sin(\frac{2\pi z}{\lambda} + wt) \bar{i} + E_{0} cos(\frac{2 \pi z}{\lambda}+wt) \bar{j}$
Let's simplify with $z = 1$. Now the xy-axis is defined by parametrization ...
0
votes
1answer
1k views
Wavefunction normalization
How do we normalize a wavefunction that's a linear combination of sines and cosines (or of $Ae^{ikx}+Be^{-ikx}$ -- they're the same, right)? One you square it, wouldn't the integrand be oscillating ...
16
votes
9answers
4k views
About the complex nature of the wave function?
1.
Why is the wave function complex? I've collected some layman explanations but they are incomplete and unsatisfactory. However in the book by Merzbacher in the initial few pages he provides an ...
4
votes
3answers
998 views
What is the relation between position and momentum wavefunctions in quantum physics?
I have read in a couple of places that $\psi(p)$ and $\psi(q)$ are Fourier transforms of one another (e.g. Penrose). But isn't a Fourier transform simply a decomposition of a function into a sum or ...
