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.
1
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1answer
294 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 ...
1
vote
1answer
21 views
No well-defined frequency for a wave packet?
There are similar questions to mine on this site, but not quite what I am asking (I think). The de Broglie relations for energy and momentum
$$ \lambda = \frac{h}{p},
\\
\nu = E/h .$$
equate a ...
6
votes
3answers
574 views
Meaning of inner product $\langle \vec{r} | \psi(t)\rangle $
I have come across the equation which comes out of the nothing in Zettili's book Quantum mechanics concepts and applications p. 167:
$$\psi(\vec{r},t) ~=~ \langle \vec{r} \,|\, \psi(t) \rangle.$$
...
2
votes
2answers
53 views
Decomposition of this wave function in eigenfunctions
I have this wave function of a system on a central potential: $V(r)$:
$$\Phi(x,y,z)=C(x+y+z)e^{-\alpha r^2}.$$
And I'm asked a few things about probabilities. I don't have problems with that, because ...
-1
votes
1answer
57 views
Problem from Sakurai about a delta-function potential [closed]
Can you help me with this problem from Sakurai:
A particle of mass m in one dimension is bound to a fixed center by an attractive delta-function potential:
$$V(x) ~= ~-a\delta(x) , \qquad ...
0
votes
1answer
70 views
Expectation value of momentum
I'm having a problem with an expectation value that doesn't seem to add up for me.
What I know is, that $\psi(\vec{r})$ is a wavefunction for a particle in three dimensions. The Hamiltonian is given ...
0
votes
1answer
76 views
Why do people say the phase oscillates in time and the amplitude stays the same but the intensity of a traveling beam does oscillate with time?
I'm confused why people say the phase oscillates in time and the amplitude stays the same (the reason for having complex numbers). But on the other hand, the intensity of a traveling beam does ...
2
votes
2answers
185 views
Text interpretation in Griffith's intro to QM
It says in Griffith's chapter 2.1, that:
$$\tag{2.14} \Psi(x,t)~=~\sum_{n=1}^{\infty}c_n\,\psi_n(x) e^{(-iE_n t/\hbar)}$$
It so happens that every solution to the (time-dependent) Schrodinger ...
0
votes
1answer
54 views
Expectation value of position in infinite square well
I'm looking for some help to a question.
I'm working in the infinite square well, and I have the wavefunction:
$$\psi(x,t=0)=A\left( i\sqrt{2}\phi_{1}+\sqrt{3}\phi_{2} \right).$$
For every time t, ...
0
votes
0answers
44 views
First-order pertubation theory
I'm having some trouble figuring this out, so I was hoping someone could help.
I need to show that the first-order pertubation of the ground state energy is not changed by the pertubation $H'$, given ...
1
vote
1answer
41 views
Infinite Potential Well Energy for Piece-wise Constant Wave Function
I'm trying to compute the expectation value of energy for a certain state in an infinite potential well but I'm getting contradictory answers.
The well has potential
\begin{align}
V(x) = \left\{
...
0
votes
0answers
49 views
Any problem at assuming the wave function as a real (rather than complex) function? [duplicate]
I'm a beginner at quantum mechanics but whenever I check the wave functions, they always have a complex factor.
I can't clearly understand because complex number is an imaginary number so it can't ...
3
votes
2answers
75 views
Momentum of particle in a box
Take a unit box, the energy eigenfunctions are $\sin(n\pi x)$ (ignoring normalization constant) inside the box and 0 outside. I have read that there is no momentum operator for a particle in a box, ...
0
votes
1answer
60 views
Physical interpretation of normalization of wave fuctions
Does normalization of wave function mean that we are getting our state vector to unit length? If that's the case what does it mean physically? Also is the underlying vector space finite dimensional? ...
0
votes
1answer
161 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 ...
2
votes
1answer
76 views
Harmonic oscillator - wavefunctions
I understand now how I can derive the lowest energy state $W_0 = \tfrac{1}{2}\hbar \omega$ of the quantum harmonic oscillator (HO) using the ladder operators. What is the easiest way to now derive ...
3
votes
3answers
112 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 ...
0
votes
1answer
60 views
What is the wave length of the entire universe?
In quantum physics, particles are also waves. Larger particles have shorter wave lengths, and macroscopic objects have extremely short wave lengths so that the wave aspect can be ignored, and ...
3
votes
3answers
426 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
1answer
688 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
2answers
62 views
Using the Normalization Condition with Wavefunction
I'm very confused with this problem and I was looking for some guidance.
$$\psi(x) = Ae^{ikx}e^{-x^2/2a^2}$$
Use the normalization condition to find A.
So I understand that you use the normalization ...
1
vote
1answer
61 views
What does the wavevector $\textbf{k}$ mean?
In Ashcroft, Mermin Solid State Physics, Eq. 17.43 is
$$
\epsilon(\textbf{k}) = \frac{\hbar^2 k^2}{2m} - e\phi(\textbf{r})
$$
where $\textbf{k}$ is the wavevector and all other symbols have their ...
2
votes
2answers
80 views
Interpretation of de Broglie wave
Until what point can the de Broglie wave be thought as a real wave?
I mean, is it made of something?
What amplitude does it have? Is it a sine wave?
How can it be related to the wavefunction of the ...
-1
votes
0answers
32 views
What values should the solved time-independent Schrodinger equation return? [closed]
I'm doing a project on Schrodinger's equation for my differential equations class. We solved the time independent function, and now we want to provide some examples of applying the equation by solving ...
1
vote
2answers
110 views
Can we measure “wavefunction” of quantum particles?
We know that there is uncertainty principle, so question: can we ever measure wavefunction of particles? I do not think this is possible, but I am not sure. I guess that everything is probabilistic. ...
0
votes
1answer
99 views
Periodic boundary condition on a Wave Function of a Particle in a Box
Until now solving the Schrodinger Equation for a particle in a box was relatively easy because the boundaries conditions imposed zero value on the wave function at the boundaries. But now I must find ...
1
vote
2answers
52 views
Time evolution of Gaussian wave packet
I'm slightly confused as to answer this question, someone please help:
Consider a free particle in one dimension, described by the initial wave function
$$\psi(x,0) = ...
0
votes
2answers
65 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
66 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 ...
0
votes
0answers
314 views
Ground state energies with fermions of same spin?
Consider two non-interacting Fermions (half-integer spin) confined in
a 'box'. Construct the anti-symmetric wavefunctions and compare the
corresponding ground-state energies of the two systems; ...
3
votes
1answer
36 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 ($k$ ...
1
vote
1answer
83 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 ...
2
votes
1answer
65 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
49 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 $t=0$?
...
0
votes
0answers
62 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
51 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 ...
0
votes
1answer
395 views
Plotting Hydrogen's $2P_{x,y,z}$ Probability Densities in MATLAB [closed]
I have spent an unreasonable amount of time trying to plot $F(r,\theta,\phi)$ plane slices in MATLAB. I want to look at $x-y,y-z,x-z$ planes. Here's the function, specifically:
...
-2
votes
1answer
718 views
How to calculate ground state wave function?
I have seen many ground state wave functions.
From where are they derived?
How can one calculate them?
Where can one find a list of all ground state wavefunctions discovered?
0
votes
1answer
114 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}
...
2
votes
2answers
147 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, ...
2
votes
2answers
107 views
Why the hydrogen radial wave function is real?
Why the hydrogen radial wave function is real?
Is it a coincidence?
0
votes
1answer
124 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, ...
1
vote
1answer
87 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
0answers
103 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
vote
2answers
95 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 ...
0
votes
3answers
627 views
Absolute value sign when normalizing a wave function
I have solved the following problem from Griffiths "Introduction to Quantum Mechanics".
Consider the wavefunction:
$\Psi (x,t) = A e^{-\lambda |x|} e^{-i\omega t} $
Normalize $\Psi$.
Now, we ...
1
vote
1answer
96 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 ...
1
vote
1answer
167 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 ...
2
votes
1answer
80 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 ...
