Partial differential equation which describes the time evolution of the wavefunction of a quantum system. It is one of the first and most fundamental equations of quantum mechanics.
14
votes
6answers
950 views
Why can we treat quantum scattering problems as time-independent?
From what I remember in my undergraduate quantum mechanics class, we treated scattering of non-relativistic particles from a static potential like this:
Solve the time-independent Schrodinger ...
20
votes
4answers
757 views
In quantum mechanics, given certain energy spectrum can one generate the corresponding potential?
A typical problem in quantum mechanics is to calculate the spectrum that corresponds to a given potential.
Is there a one to one correspondence between the potential and its spectrum?
If the ...
4
votes
5answers
383 views
How isolated must a system be for it's wave function to be considered not collapsed?
As an undergrad I was often confused over people's bafflement with Schodinger's cat thought experiment. It seemed obvious to me that the term "observation" referred to the Geiger counter, not the ...
2
votes
1answer
237 views
Wavefunction in quantum mechanics and locality
Every wavefunction of a form $\Psi(x)$ can be described as a superposition of multiple free particle solutions.
We can see the following Fourier transform:
$$ \psi(x) = \int e^{ik\cdot x} \psi(k) dk ...
10
votes
2answers
683 views
Schrodinger equation in spherical coordinates
I read a paper on solving Schrodinger equation with central potential, and I wonder how the author get the equation(2) below. Full text.
In Griffiths's book, it reads
...
5
votes
1answer
779 views
4
votes
2answers
301 views
Does String theory say that spacetime is not fundamental but should be considered an emergent phenomenon?
Does String theory say that spacetime is not fundamental but should be considered an emergent phenomenon?
If so, can quantum mechanics describe the universe at high energies where there is no ...
2
votes
2answers
440 views
What math is needed to understand the Schrödinger equation?
If I now see the Schrödinger equation, I just see a bunch of weird symbols, but I want to know what it actually means. So I'm taking a course of Linear Algebra and I'm planning on starting with PDE's ...
3
votes
2answers
284 views
Galilean invariance of the Schrodinger equation
I am only asking this question so that I can write an answer myself with the content found here:
http://en.wikipedia.org/wiki/User:Likebox/Schrodinger#Galilean_invariance
and here:
...
7
votes
2answers
395 views
Solving the Schrödinger equation for the double-slit experiment
I'm not sure if this is the right place to ask a question about the Schrödinger equation, but I'll take my chances anyway. Basically, I would like to know how one can set up a potential function that ...
5
votes
3answers
334 views
Nonlinear dynamics beneath quantum mechanics?
Yesterday I asked whether the Schroedinger Equation could possibly be nonlinear, after reviewing the answers and material given to me in that thread I feel like my question were adequately answered.
...
2
votes
2answers
284 views
Plotting $\psi$ for finite square well potential
Lets say we have a finite square potential well like below:
This well has a $\psi$ which we can combine with $\psi_I$, $\psi_{II}$ and $\psi_{III}$. I have been playing around and got expressions ...
2
votes
1answer
222 views
Explanation of equation that shows a failed approach to relativize Schrodinger equation
I'm reading the Wikipedia page for the Dirac equation:
$\rho=\phi^*\phi\,$
......
$J = -\frac{i\hbar}{2m}(\phi^*\nabla\phi - \phi\nabla\phi^*)$
with the conservation of probability ...
2
votes
2answers
306 views
Correct application of Laplacian Operator
Not a physicist, and I'm having trouble understanding how to apply the Laplacian-like operator described in this paper and the original. We let:
$$ \hat{f}(x) = f(x) + \frac{\int H(x,y)\psi(y) ...
1
vote
2answers
153 views
$\nabla$ and non-locality in simple relativistic model of quantum mechanics
In Wavefunction in quantum mechanics and locality, wavefunction is constrained by $H = \sqrt{m^2 - \hbar^2 \nabla^2} $, and taylor-expanding $H$ results in:
$$ H = \dots = m\sqrt{1 - \hbar^2/m^2 ...
1
vote
1answer
162 views
Complete set and Klein-Gordon equation
In http://www.physics.ucdavis.edu/~cheng/teaching/230A-s07/rqm2_rev.pdf, it says that when there is some external potential, the Klein-Gordon equation is altered, and it says the following:
The ...
5
votes
2answers
2k views
Solving one dimensional Schrodinger equation with finite difference method
Consider the one-dimensional Schrodinger equation
$$-\frac{1}{2}D^2 \psi(x)+V(x)\psi(x)=E\psi(x)$$
where $D^2=\dfrac{d^2}{dx^2},V(x)=-\dfrac{1}{|x|}$.
I want to calculate the ground state ...
4
votes
2answers
427 views
Use of Operators in Quantum Mechanics
I understand the form of operators in use for quantum mechanics such as the momentum operator:
$$\hat{\text{P}}=-ih\frac{d}{dx}$$ My question is in what ways can I use it and what am I getting back? ...
4
votes
2answers
2k views
Zero probability of finding an electron in the nucleus
One and the same electron in a p orbital and taking part in a common π (pi) bond has two lobes visualized as connecting through the nucleus. There is however zero probability of finding an electron at ...
3
votes
1answer
138 views
Schrödinger equation for a harmonic oscillator
I have came across this equation for quantum harmonic oscillator
$$
W \psi = - \frac{\hbar^2}{2m}\frac{d^2\psi}{dx^2} + \frac{1}{2} m \omega^2 x^2 \psi
$$
which is often remodelled by defining a new ...
1
vote
2answers
345 views
Schrödinger's equation, time reversal, negative energy and antimatter
You know how there are no antiparticles for the Schrödinger equation, I've been pushing around the equation and have found a solution that seems to indicate there are - I've probably missed something ...
0
votes
0answers
43 views
Wave equations for two intervals at Potential step
Lets say we have a potential step as in the picture:
In the region I there is a free particle with a wavefunction $\psi_I$ while in the region II the wave function will be $\psi_{II}$.
Let me ...
0
votes
1answer
385 views
Solving the time independent Schrodinger equation: Does a complex solution make sense?
In my notes, I have the Time Independent Schrodinger equation for a free particle
$$\frac{\partial^2 \psi}{\partial x^2}+\frac{p^2}{\hbar^2}\psi=0\tag1$$
The solution to this is given, in my notes, ...
0
votes
1answer
82 views
a positive potential as $ x \rightarrow \infty $
let us suppose i can calculate the asymptotic of any potential $ V(x) $ in one dimension , and that i manage to prove that $ V(x) \ge 0 $ as $ x \rightarrow \infty $
could i conclude taht if or big ...
0
votes
1answer
263 views
Two-state system problem
Given a 2-state system with (complete set) orthonormal eigenstates $u_1, u_2$ with eigenvalues $E_1, E_2$ respectively, where $E_2>E_1$, and there exists a linear operator $\hat{L}$ with ...
-1
votes
2answers
141 views
Show that the energy levels of a particle in a specific potential are $E_n=(n+\frac{1}{2})h\omega-\frac{1}{2}\frac{F^2}{m\omega^2}$ [closed]
A particle of mass m moves on the x-axis under the influence of the potential
$$V(x)=\frac{1}{2}m\omega^2x^2+Fx$$
Can anyone help me, using Schrödinger's equation in one dimension that the energy ...
