New answers tagged wavefunction
0
votes
Another Entanglement Question - Can you tell if the wave function of an entangled particle is collapsed?
First, a discussion of collapse. The motion of a quantum system in general depends on what happens to all of its possible states, e.g. - during a single particle interference experiment, all of the ...
- 9,280
1
vote
Accepted
Why does $\langle x | f \rangle = f(x) $?
In Shankar's book, the point is to determine the components of $|\psi\rangle$ in the position basis. If we label the components as $\psi(x)$, then we want
$$|\psi\rangle=\int\psi(x')|x'\rangle\ \text ...
- 58.2k
2
votes
What is the meaning of this complex derivative with respect to a wave function?
The derivatives are presumably (equal to) Dolbeault derivatives
$$ \begin{align}\frac{\partial}{\partial\psi}~=~&\frac{1}{2}\left(\frac{\partial}{\partial {\rm Re}\psi}-i\frac{\partial}{\partial {\...
- 209k
3
votes
Another Entanglement Question - Can you tell if the wave function of an entangled particle is collapsed?
No, you can't tell what has happened far away if all you have access to is the local system, even if your local system is entangled with the far-away system. This is a consequence of the "no-...
- 1,874
2
votes
Another Entanglement Question - Can you tell if the wave function of an entangled particle is collapsed?
Any time you make a quantum observation, the wave function of your system collapses in the sense that it gets projected onto the eigenspace of your observable that corresponds to the observed outcome. ...
- 16.3k
7
votes
Wrong explanation for why "electron can't exist in the nucleus"?
Electrons do "spend time" inside the nucleus, just as they "spend time" in other spherical regions of a similar size. You can see that from the fact that the $1s$ orbital wave ...
- 28.2k
5
votes
Wrong explanation for why "electron can't exist in the nucleus"?
Everything @BioPhysicist is correct, but in addition:
Your argument is semi-classical, quantum mechanics is non-relativistic (there is no $c$ in the Schrödinger Eq.), and the problem involves ...
- 36.7k
2
votes
Understanding the parabolic state of a quantum particle in the infinite square well
As explained in previous answers, your wave function belongs to the full Hilbert space $L^2$, and the domain of $H$, but not to the domain of $H^2$. In general, unbounded operator (like $H$ or $H^2$) ...
- 13.5k
8
votes
Accepted
Wrong explanation for why "electron can't exist in the nucleus"?
When are asked about why an electron cannot fall into the nucleus...
This is a common "problem" when talking about the issues with the classical picture of an electron orbiting the nucleus, ...
- 58.2k
11
votes
Accepted
Understanding the parabolic state of a quantum particle in the infinite square well
Before we can answer the question, we need a little bit more mathematical clarity here. However, we won't be fully rigorous and leave out details which are not of interest for the question.$^\ddagger$
...
- 8,375
3
votes
Accepted
Detect Global Phase
In your example, you're assuming a wavefunction of the form
$$\psi(x) = e^{i\theta}\cos(kx), $$
then the probability density is simply
$$P(x) = |\psi(x)|^2=\psi\psi^* = |e^{i\theta}|\cos^2(kx)=\cos^2(...
- 2,397
5
votes
Understanding the parabolic state of a quantum particle in the infinite square well
Barring the (now corrected) mistake of the omission of part of eigenvectors,
the point is quite trivial: here one is referring to two different notions of energy observable but using the same name!
...
- 75.6k
4
votes
Understanding the parabolic state of a quantum particle in the infinite square well
Let's be clearer with the essence of your problem, now that the other answerer brought to your attention that you were missing the cosines.
Your state is $\left<x|\psi\right>=\sqrt{\frac{15}{16\...
- 10.2k
7
votes
Understanding the parabolic state of a quantum particle in the infinite square well
There's a simple error in your $\psi_n$ which is screwing you up. In general, the form of the eigenstates $\psi_n(x;x_o,L)$ for a well of length $L$ starting at $x_o$ is
$$
\psi_n(x;x_o,L) \propto \...
- 902
0
votes
Are there any examples of superposition other than double-slit (or similar) experiment, which we can actually visualize?
There are many kinds of interferometers that aren't that difficult to visualize. Some of the simplest ones are the Michelson interferometer and the Mach-Zehnder interferometer
These are basically ...
- 28.8k
3
votes
Can a wave function discontinuous in the time variable be a solution of the Schrödinger equation?
In principle, why not? Just make sure your Hamiltonian has a term proportional to $\delta(t)$. As an example think of a particle that receives an instant kick at $t=0$. At $t<0$ it was in the state ...
- 4,039
2
votes
Accepted
How do I calculate the probability distribution of momentum assuming that my instrument has a small spatial extension?
One way to carry out this experiment and illustrate some quantum strangeness is diffraction through a pinhole. You take a laser and point it at a screen with a slit in it. Some light hits the screen. ...
- 42.7k
4
votes
Accepted
Does measuring a quantum object collapse the wave function even if the particle is not found in the position where it was measured?
The "collapse of the wave function" is a very unphysical concept: It was invented within the Copenhagen Interpretation by people who tried to make sense of Quantum Mechanics, and who ...
1
vote
Does measuring a quantum object collapse the wave function even if the particle is not found in the position where it was measured?
You write:
Properties of quantum objects are determined by a wave function.
Not exactly. The wavefunction represents the evolution of the system. Sometimes that evolution involves what is happening ...
- 9,280
3
votes
Does measuring a quantum object collapse the wave function even if the particle is not found in the position where it was measured?
We are talking about a statistical law here. The probability of finding the particle in region $[x+\Delta x]$:
$$
P(x < X < x+\Delta x)=|\psi(X)|^2\Delta x=w
$$
This means that, after performing ...
- 61.8k
0
votes
Correct way to take complex conjugate of the Schrodinger equation
The first approach is correct.
$H$ is an operator that acts on the wave function, so it doesn't commute with it. It seems like in the second approach you (incorrectly) mixed up the hermitian conjugate ...
- 1,925
0
votes
Double slit experiment with two sources
Before discussing visible light and electrons I want to point out a particularly vivid example of obtaining interference effect with multiple sources: a phased array
A phased array antenna for ...
- 22.2k
0
votes
Physical reason why the derivative of a wavefunction has to be continuous?
You need second derivative to exist because that is the kinetic energy. And for that, the first derivative must be continuous!
This is the physical reason.
1
vote
Double slit experiment with two sources
From a typical high school physics textbook view your question is interesting ... but using a more modern understanding ... maybe taking a quantum optics course ... a new perspective will yield the ...
- 2,760
1
vote
Non-interacting wavefunction for indistinguishable particles
You end up with
$$1=A^2[2\pm2(\int\psi_a(\vec r)\psi_b^*(\vec r) d^3r)^2]$$
The integral is $\delta_a^b$, because the individual wave functions are orthonormal. Notice that when $a=b$, then $A$ can ...
- 1,229
0
votes
What is the cardinality of the set of all possible wave functions?
Strictly speaking, L^2-space really consists of equivalence classes of functions. Two functions represent the same L^2-function if the set where they differ has measure zero. It is not hard to see ...
- 8,983
12
votes
Accepted
What is the cardinality of the set of all possible wave functions?
Actually the wavefunctions are the elements of a $L^2(R^n)$ space. That space is separable, so to fix an element you have to fix a sequence of complex numbers. The fact that the sequence must converge ...
- 75.6k
-6
votes
Question about Bohr/Einstein recoiling slits experiment
Feynman is giving you an awful piece of misinformation here that serves very little educational purpose. First things first: There are no particles in quantum mechanics. What we are measuring are ...
- 3,137
Top 50 recent answers are included