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.
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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, ...
7
votes
2answers
230 views
Superconducting Wavefunction Phase (Feynman Lectures)
In Volume 3, Section 21-5 of the Feynman lectures (superconductivity), Feynman makes a step that I can't quite follow. To start, he writes the wavefunction of the ground state in the following form ...
3
votes
1answer
310 views
Expectation values-Wavefunction
I'm a bit puzzled about an excercise in which I have to find the expectation values for position and momentum. Normally this should be pretty easy but in this case I just don't get the point.
...
5
votes
3answers
367 views
Meaning of $\int \phi^\dagger \hat A \psi \:\mathrm dx$
While analysing a problem in quantum Mechanics, I realized that I don't fully understand the physical meanings of certain integrals. I have been interpreting:
$\int \phi^\dagger \hat A \psi ...
2
votes
3answers
220 views
Is this interpretation of $\psi=\frac{1}{\sqrt{\pi a^{3}}}e^{-r/a}$ correct?
Apologies if this is stating the obvious, but I'm a non-physicist trying to understand Griffiths' discussion of the hydrogen atom in chapter 4 of Introduction to Quantum Mechanics. The wave equation ...
1
vote
2answers
128 views
What does the quantum state of a system tell us about itself?
In quantum mechanics, quantum state refers to the state of a quantum
system. A quantum state is given as a vector in a vector space, called
the state vector. The state vector theoretically ...
5
votes
2answers
311 views
Does quantum mechanics allow faster than light (FTL) travel?
Let's suppose I initially have a particle with a nice and narrow wave function[1] (I will leave these unnormed):
$$e^{-\frac{x^2}{a}}$$
where $a$ is some small number (to make it narrow). Let's also ...
1
vote
0answers
29 views
What methods exist for us to measure the position and momentum of atoms that make up molecules?
In reference to this paper, http://iopscience.iop.org/1355-5111/8/1/014, we are able to localize atoms using homodyne measurement. Would it be too naive to consider we can measure the position of ...
7
votes
2answers
254 views
Was uncertainty principle inferred by Fourier analysis?
I would like to know: did Heisenberg chance upon his Uncertainty Principle by performing Fourier analysis of wavepackets, after assuming that electrons can be treated as wavepackets?
3
votes
2answers
146 views
Interpretation of $e|\psi|^2$ as electron density
In solid state physics the electron density is often equated to $e|\psi|^2$. However, the Sakurai says (Chapter 2.4, Interpretation of the Wave Function, p. 101) that adopting such a view leads "to ...
1
vote
2answers
346 views
What's the physical significance of the inner product of two wave functions in quantum region?
I am a reading a book for beginners of the quantum mechanics. In one section, the author shows the inner product of two wave functions $\langle\alpha\vert\beta\rangle$. I am wondering what's the ...
2
votes
2answers
359 views
Non-Degeneracy of Eigenvalues of Number Operator for Simple Harmonic Oscillator [duplicate]
Possible Duplicate:
Proof that the One-Dimensional Simple Harmonic Oscillator is Non-Degenerate?
I'm trying to convince myself that the eigenvalues $n$ of the number operator ...
1
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1answer
127 views
How is wavefunction probability redistributed after partial wavefunction collapse?
Suppose I set up the double-slit experiment using photons as my particle. Behind the left slit I place a beam splitter that points some of the light off in the direction of a camera (represented as ...
8
votes
2answers
256 views
Wavefunction collapse and gravity
If gravity can be thought of as both a wave (the gravitational wave, as predicted to exist by Albert Einstein and certain calculations) and a particle (the graviton), would it make sense to apply ...
2
votes
1answer
90 views
Confused over the presence of 2 expressions for $\Psi(x,t)$
I'm following Griffiths' Introduction to Quantum Mechanics, and I see that he's got 2 different expressions for $\Psi(x,t)$. One of them is ...
1
vote
1answer
430 views
Plane wave expansion in cylindrical coordinates
I am trying to solve scattering problem in 2D and got to expand the wave function in cylindrical system which comes out to be Hankel function. Can you tell me how to expand the plane wave $\exp(i ...
1
vote
2answers
144 views
Does quantum mechanics predict instantaneous action at a distance even without entanglement?
The suggestion that quantum mechanics implies that instantaneous action at a distance occurs is normally based on the contention that this follows from the entanglement of particles that share a ...
0
votes
1answer
112 views
Quantum Mechanics - Orthonormality of $d_{xz}$ and $d_{yz}$ Orbitals [closed]
Recall that all spherical harmonics $Y_{l,m}$ are orthornormal. Show that the $d_{xz}$ and $d_{yz}$ orbitals are both orthogonal to each other and normalized. In answering this question, DO NOT ...
1
vote
1answer
160 views
Quantum Mechanics - The Normalization of $\psi_{3,1,1}$
Show that the hydrogen atomic wavefunction $\psi_{3,1,1}$ is normalized, and that it is orthogonal to $\psi_{3,1,−1}$.
I'm not sure if I'm supposed to consider the radial part. I can show that ...
0
votes
2answers
269 views
Meaning of instantaneous probability densities in time dependent wavefunctions
For a time dependent wavefunction, are the instantaneous probability densities meaningful? (The question applies for instances or more generally short lengths of time that are not multiples of the ...
3
votes
3answers
260 views
How to compute the expectation value $\langle x^2 \rangle$ in quantum mechanics?
$$\langle x^2 \rangle = \int_{-\infty}^\infty x^2 |\psi(x)|^2 \text d x$$
What is the meaning of $|\psi(x)|^2$? Does that just mean one has to multiply the wave function with itself?
1
vote
2answers
469 views
Wave function of Hydrogen Atom
Wavefunction of a Hydrogen atom is expressed in eigenfunctions as:
$$\psi(\boldsymbol r,t=0)=1/\sqrt{14}(2\psi_{100}(\boldsymbol r)-3\psi_{200}(\boldsymbol r)+\psi_{322}(\boldsymbol r) ).$$
Is ...
7
votes
3answers
256 views
If superposition is possible in QM, why do we often assume systems are already in their eigenstates?
My understanding is that an arbitrary quantum-mechanical wavefunction can be written as a linear combination of eigenfunctions of some Hermitian operator, most commonly the Hamiltonian; when a ...
0
votes
4answers
409 views
What does superposition mean in quantum mechanics?
What does superposition mean in quantum mechanics?
When I say $A+B=C$ (forces). I can mean push something with force $A$ + force $B$ together, and that is same as I push it with force $C$.
But when ...
1
vote
1answer
319 views
Schrödinger function: Separable wave function with even potential function of x
I have done the Problem 2.1 in Griffiths' quantum mechanics,
and it seems not making sense to me.
What if the wave function isn't symmetric at all?
Then obviously the proof doesn't work. The ...
2
votes
4answers
306 views
If wave packets spread, why don't objects disappear?
If you have an electron moving in empty space, it will be represented by a wave packet. But packets can spread over time, that is, their width increases, with it's uncertainty in position increasing. ...
0
votes
0answers
168 views
Force of a particles on a Potential Barrier [closed]
A particle confined by a potential wall exerts some pressure on it. More specifically, suppose that the particle moves in this potential:
$$V(x) ~=~\left\{ \begin{array}{lcc}\text{finite ...
2
votes
1answer
1k views
Bound States in a Double Delta Function Potential [closed]
Let $V(x) = −u \delta(x) - v \delta(x − a)$ where $u, v > 0$ correspond to a potential with two $\delta$ wells. Let $v > u$. If $a$ is very large, there is certainly a bound state: the particle ...
2
votes
1answer
72 views
Does wavefunction reach its largest peak near(not in) the classical forbidden region?
As we can see in the picture in this website:
http://ctz116.ust.hk/xyli2/images/animation/quchem73.html
It's strange that the bound state wavefunction always reach its largest peak near the boundary ...
1
vote
1answer
43 views
How to compare differences in waves?
I have a series of waves that I would like to compare to one another. The measurements are two-dimensional with time on the x-axis and an intensity measurement on the y-axis.
I'd like some way of ...
4
votes
1answer
177 views
Boundary conditions from single-valuedness of spherical wavefunctions
This question is a follow-up to David Bar Moshe's answer to my earlier question on the Aharanov-Bohm effect and flux-quantization. What I forgot was that it is not the wavefunction that must be ...
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votes
2answers
98 views
Wave function of IQH and FQH electrons
What are the wave functions of the ground state of Integer Quantum Hall (IQH) and Fractional Quantum Hall (FQH) electrons?
2
votes
3answers
209 views
How do I integrate $\frac{1}{\Psi}\frac{\partial \Psi}{\partial x} = Cx$
How do I integrate the following?
$$\frac{1}{\Psi}\frac{\partial \Psi}{\partial x} = Cx$$
where $C$ is a constant.
I'm supposed to get a Gaussian function out of the above by integrating but don't ...
3
votes
3answers
223 views
Can a wavefunction be solved to any arbitrary precision, given enough computer time?
I learned that the wavefunction for the hydrogen atom can be solved analytically (we did the derivation in class), but that for more complicated atoms it is "impossible" to solve and that only ...
2
votes
1answer
68 views
What does $\psi_j(r_i)$ mean?
I have a mean-field Hamiltonian for N electrons. The mean-field potential felt by electron $i$ at position ${\bf r}_i$ is given by
$V^{(i)}_{int}({\bf r}_i)=\sum_{j\ne i}|\psi_j({\bf r}_i)|^2$
I ...
0
votes
0answers
61 views
Ultrashort Optical Pulses [closed]
If an ultrashort optical pulse has a complex wavefunction with central frequency corresponding to a certain wavelength and a Gaussian envelope of RMS width of a certain time period, how can I ...
1
vote
2answers
139 views
Pulsed Spherical Wave
Can somebody help show me how a pulsed spherical wave has a wavefunction of the form U(r,t) = (1/r)a(t-r/c), where a(t) is an arbitrary function, r is the radius of the spherical wave, t is time, and ...
3
votes
1answer
334 views
Finding $\psi(x,t)$ for a free particle starting from a Gaussian wave profile $\psi(x)$
Consider a free-particle with a Gaussian wavefunction,
$$\psi(x)~=~\left(\frac{a}{\pi}\right)^{1/4}e^{-\frac12a x^2},$$
find $\psi(x,t)$.
The wavefunction is already normalized, so the next thing to ...
3
votes
1answer
325 views
Even and Odd States of a 1D finite potential well
Is it possible for a particle trapped in a 1D finite potential well to evolve from a even state to an odd state and vice-versa? Why?
3
votes
2answers
466 views
How do I figure out the probability of finding a particle between two barriers?
Given a delta function $\alpha\delta(x+a)$ and an infinite energy potential barrier at $[0,\infty)$, calculate the scattered state, calculate the probability of reflection as a function of ...
2
votes
1answer
154 views
Considering the wave function is not 'real', what is interfering?
I find the idea of the wave function being 'just' a collection of numbers (probabilities) quite alluring, and elegant in explaining away the whole 'collapse' business (see Luboš' answer to this ...
1
vote
4answers
775 views
Reason for the Gaussian wave packet spreading
I have recently read how the Gaussian wave packet spreads while propagating.
see:
http://en.wikipedia.org/wiki/Wave_packet#Gaussian_wavepackets_in_quantum_mechanics
Though I understand the ...
5
votes
1answer
198 views
Relativistic contraction for a wave packet and uncertainty on momentum
Consider an electron described by a wave packet of extension $\Delta x$ for experimentalist A in the lab. Now assume experimentalist B is flying at a very high speed with regard to A and observes the ...
1
vote
2answers
3k views
Sinusoidal Wave Displacement Function
I am learning about waves (intro course) and as I was studying Wave Functions, I got a little confused.
The book claims that the wave function of a sinusoidal wave moving in the +x direction is as ...
2
votes
1answer
135 views
What does the notation $|x_1,x_2\rangle$ mean?
I would like clarification on an equation in the paper "Free matter wave packet teleportation via cold-molecule dynamics", L. Fisch and G. Kurizki, Europhysics Letters 75 (2006), pp. 847-853, DOI: ...
2
votes
2answers
124 views
Wave Function Statistical Interpretation vs Oscillation Interpretation
Can the wave function solution to Schrodinger's Equation be interpreted as an oscillation between all possible measurements (obviously with some type of weighting that would describe the shape of the ...
1
vote
4answers
529 views
Why is wave function so important?
I am almost sure that the wave function is the most important figures in modern physics book.
On the other hand I know that wave function even do not have a physical meaning it self alone!
Why is ...
6
votes
7answers
454 views
Is it wrong to talk about wave functions of macroscopic bodies?
Does a real macroscopic body, like table, human or a cup permits description as a wave function? When is it possible and when not?
For example in the "Statistical Physics, Part I" by Landau & ...
3
votes
1answer
261 views
wavefunction collapse and uncertainty principle
We all know that wavefunction collapse when it is observed. Uncertainty principle states that $\sigma_x \sigma_p \geq \frac {\hbar}{2}$. When wavefunction collapse, doesn't $\sigma_x$ become $0$?, as ...
2
votes
5answers
218 views
wave superposition of electrons and quarks
Is quantum wave superposition of electrons and quarks possible?
If not, can different types of elementary particles be mixed in wave superposition?
