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.
2
votes
1answer
134 views
Why don't cancelling wavefunctions for two different particles give zero total wavefunction?
Let $\left|a\right>=e^{i(kx-\omega t)}$， $\left|b\right>=-e^{i(kx-\omega t)}$ be two neutral particles in the 1D free space without any interaction. Then ...
3
votes
4answers
250 views
Does the wave nature of a particle refer to the wave function?
In quantum mechanics when we talk about the wave nature of particles are we referring in fact to the wave function? Does the wave function describes the probability of finding a particle (ex: ...
1
vote
2answers
253 views
Can we impose a boundary condition on the derivative of the wavefunction through the physical assumptions?
Consider the Schrödinger equation for a particle in one dimension, where we have at least one boundary in the system (say the boundary is at $x=0$ and we are solving for $x>0$). Sometimes we want ...
6
votes
1answer
405 views
Must the derivative of the wave function at infinity be zero?
I came across a problem in Griffiths where the derivative of the wave function (with respect to position in one dimension) evaluated at $\pm\infty$ is zero. Why is this? Is it true for any function ...
3
votes
1answer
252 views
Help me understand the first equation in Landau & Lifshitz's Quantum Mechanics
While I've covered a basic course in Quantum Mechanics, I'm self-studying Landau & Lifshitz's book to help me understand what's going on.
Unfortunately, I'm stuck on the very first equation in ...
1
vote
1answer
705 views
what is phase angle of wave function $\phi \,$?
this is wave function:
$$\Psi{(\vec r, t)}=\Psi_0 e^{i(\vec k \cdot \vec r-\omega t)}$$
$$\Psi{(\vec r, t)}=A e^{i(\phi + \vec k \cdot \vec r-\omega t)}$$.
what is phase angle $\phi$ of wave ...
1
vote
1answer
315 views
How Represent Waves via Complex Numbers?
i try to finished my thesis, (Just have a problem with the wave mechanics)
this is wave function:
$$\Psi(\vec x, t)=A\exp{i(\phi+\vec k.\vec x-\omega t)}$$
In mathematics, the symbol $i$ is ...
1
vote
1answer
287 views
How Light or Water Intensity is equal to square modulus of wave function of Light or Water Waves $I=|\psi|^2 \,$?
I've seen the Wave Function as a psi $\Psi$ $\psi$.
And always heard that the wave function is the Complex Number as Imaginary and real number.
But I've never seen it
I've never seen components of ...
0
votes
2answers
207 views
matter wave and wave function
Is there any mathematical relationship between matter wave (or de Broglie wave) and wave function?
Also, does each type of particle (e.g. photon, electron, positron etc.) have its own unique wave ...
2
votes
1answer
973 views
Angular momentum operator and expectation values
I was reading some notes and it says that $\langle L_z^2\rangle=\langle L^2\rangle$ IFF the system is radially symmetric. I can see that in order that the LHS of the statement implies that $\langle ...
1
vote
1answer
319 views
Relationship between classical electromagnetic wave frequency and quantum wave function + de broglie frequency
As it is.
As I study through classical mechanics and quantum mechanics, I began to wonder whether there is a relationship between classical electromagnetic wave frequency and quantum wave function ...
1
vote
1answer
281 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 ...
0
votes
1answer
344 views
Wave packets v.s. wave trains
Could someone please explain the difference between a wave packet and a wave train? I have rummaged around online but have not been able to find a definitive definition.
3
votes
1answer
343 views
Where does the wave function of the universe live? Please describe its home
Where does the wave function of the universe live?
Please describe its home.
I think this is the Hilbert space of the universe. (Greater or lesser, depending on which church you belong to.)
Or maybe ...
1
vote
3answers
328 views
Why can't we know the speed, $\vec{v}(t)$, and position, $\vec{r}(t)$, of an electron (the two) at the same time $t$?
I've read something about this and I conclude that it happens because of the uncertainty principle. But I don't understand very well the meaning of that.
I mean, it's very abstract that the speed, ...
3
votes
1answer
122 views
What does the appearance of a classical particle fundamentally reduce to?
I've been reading an article that describes what seems to be a classical particle as a regularity in the global wavefunction over a quantum configuration space:
When you actually see an electron ...
3
votes
2answers
364 views
Is the free electron wavefunction stable?
The wavefunction of a free electrons is variously described as a plane wave or a wave packet. I am fairly happy with the wave packet, as it is localised.
But if we change to the electron's rest ...
1
vote
0answers
150 views
Analytic form of the normalization constant for Laughlin wavefunction
Is there any analytic form of the normalization constant for Laughlin wavefunction
$$\prod_{i < j} (z_i-z_j)^{1/\nu} e^{-\sum_i |z_i|^2/4}$$
where $\nu$ is the filling factor?
4
votes
1answer
34 views
Tip of a spreading wave-packet: asymptotics beyond all orders of a saddle point expansion
This is a technical question coming from mapping of an unrelated problem onto dynamics of a non-relativistic massive particle in 1+1 dimensions. This issue is with asymptotics dominated by a term ...
5
votes
3answers
523 views
Electrons - What is Waving?
If an electron is a wave, what is waving?
So many answers on the internet say "the probability that a particle will be at a particular location"... so... the electron is a physical manifestation of ...
3
votes
2answers
318 views
Is the electron wave function defined during photon emission
I have heard the term quantum leap to describe the (instantaneous?) transition from a higher energy orbital to a lower energy orbital. Yet, I understand that this transition time has now been ...
5
votes
3answers
143 views
Time Varying Potential, series solution
Suppose we have a time varying potential $$\left( -\frac{1}{2m}\nabla^2+ V(\vec{r},t)\right)\psi = i\partial_t \psi$$ then I want to know why is the general solution written as $\psi = ...
-2
votes
1answer
681 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?
1
vote
1answer
238 views
Solving Schrödinger's equation for a specific potential
I am trying to solve this differential equation:
$$-\chi''(\epsilon)+\Big[\epsilon^2+\frac{2F}{hw}\sqrt{\frac{h}{hw}}\epsilon \Big]\chi(\epsilon)=\mu\chi(\epsilon) \tag1$$
This was found ...
0
votes
2answers
482 views
Matter waves and de Broglie wave length
The wavelength of a particle of momentum p is calculated using De Broglie relation.
The de Broglie relation was postulated for what is called a matter waves. Now according to the statistical ...
2
votes
1answer
421 views
Wave function of hydrogen atom including spin of nucleus
How do I write the wave function of hydrogen atom taking into consideration of nucleus spin? For example consider $2S_{\frac{1}{2}}$ state with nucleus spin $I$, then wave function ...
1
vote
3answers
399 views
One dimensional Schrödinger equation equation with initial condition, finding the probability of the particle's future position
A particle of mass $m$ moves freely in the interval $[0,a]$ on the $x$ axis. Initially the wave function is:
$$f(x)=\frac{1}{\sqrt{3}}\operatorname{sin}\Big( \frac{\pi x}{a} ...
1
vote
1answer
765 views
Relation between wavenumber and propagation constant
What is the exact difference between wavenumber and propagation constant in an electromagnetic wave propagating in a medium such as a transmission line, cause i am a bit confused. Does it have to do ...
0
votes
1answer
82 views
How are particle simplices associated into complex particles?
Nonfundamental particles are seen as made up of fundamental particles (in whatever specific theory).
consider the simple case of 2 simplex particles (subscript 1 and 2) which form a complex particle ...
1
vote
2answers
168 views
Expressing a particle's matter wave in terms of its momentum
I'm following Zettili's QM book and on p. 39 the following manipulation is done,
Given a localized wave function (called a wave packet), it can be expressed as $$\psi(x,t) = \frac{1}{\sqrt{ 2 \pi}} ...
3
votes
3answers
340 views
Smoothness constraint of wave function
Is there anything in the physics that enforces the wave function to be $C^2$? Are weak solutions to the Schroedinger equation physical? I am reading the beginning chapters of Griffiths and he doesn't ...
2
votes
1answer
758 views
How to calculate time evolution of a wave function in an 1D infinite square well potential?
A particle in an infinite square well has an initial wavefunction
$$\psi (x,0) ~=~ Ax(a-x) \qquad \mathrm{for}\qquad 0\leq x\leq a.$$
Now the question is to calculate $\psi (x,t)$.
I have ...
1
vote
1answer
691 views
What does $\Psi^*$ mean in Schrodinger's Equation?
I am not a physics student. In one of my courses, some fundamental concepts of Quantum mech were needed, so i was gng through them when i stumbled upon this
It says
$$\text{probability} = ...
0
votes
3answers
326 views
How can I show that an arbitrary wavefunction in a 1D SHO is periodic in time?
I want to show that an arbitrary wavefunction $f$ in a one dimensional harmonic potential reproduces itself after a period T up to a phase factor: $f(x,t+T)=Af(x,t)$, $|A|=1$
I am not sure if this ...
2
votes
3answers
273 views
What is the rationale behind representing a state function by a complex valued function in QM?
What is the rationale behind representing a state function of an electron with a complex valued function $\Psi$. If only the probabilistic argument was required then why not represent it with just a ...
0
votes
1answer
376 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:
...
0
votes
0answers
310 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; ...
2
votes
1answer
388 views
Transmission and reflection
What is the transmission amplitude of a wavefunction $\phi(x)=e^{ikx}(\tanh x -ik)$? I would have thought that it is $\tanh x -ik$ since this is the factor associated with the forward travelling ...
3
votes
1answer
142 views
Expected value inequality
Why is $\langle p^2\rangle >0$ where $p=-i\hbar{d\over dx}$, (noting the strict inequality) for all normalized wavefunctions? I would have argued that because we can't have $\psi=$constant, but ...
2
votes
2answers
789 views
Speed of a particle in quantum mechanics: phase velocity vs. group velocity
Given that one usually defines two different velocities for a wave, these being the phase velocity and the group velocity, I was asking their meaning for the associated particle in quantum mechanics.
...
2
votes
4answers
228 views
Are Everettian branchings global or local?
Everett's theory of quantum mechanics is about the wavefunction of the whole universe holistically. If a branching occurs very far away at the Andromeda galaxy, do I also branch? Are branchings global ...
0
votes
1answer
318 views
Weird operator and wavefunctions
How can one show that $\int_{-\infty}^{\infty}\psi^*(x)(d/dx+\tanh x)(-d/dx+\tanh x)\psi(x) dx=\int_{-\infty}^{\infty} |(d/dx+\tanh x)\psi(x)|^2 dx$, where $\psi$ is normalized?
2
votes
1answer
753 views
Probability current
Conservation of probability: Suppose a wavefunction has ${\partial \mathbb P \over \partial t} = -t f(x,t)$ and ${\partial j \over \partial x} = i f(x,t)$. How does it follow that ${\partial \mathbb P ...
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
262 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
316 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
111 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
306 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
260 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
191 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 ...
