Questions tagged [wavefunction]
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. DO NOT USE THIS TAG for classical waves.
2,278
questions
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0answers
32 views
Asymmetric delta potential well modelling wave function [closed]
I'm trying to model the wave function for an asymmetric delta function potential well, in which the left side of the well is at a potential of $0$, however the right side of the well has been moved ...
0
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0answers
30 views
How to get Airy differential equation?
A particle with mass m is under the following potential:
$$V(x) = \begin{align}
0 |x|\leq L ;
c(|x|-L) |x|>L
\end{align}$$
and the schrodinger equation:
$$ \psi (x)'' + \frac {2m}{\hbar^2} ...
0
votes
2answers
39 views
Time-dependent state probability harmonic oscillator [closed]
For my homework i am considering a harmonic oscillator which´s wavefunction at $t=0$ is the superposition of the eigenstates $\psi_n$.
$$
\psi(x,t=0) = \sum\nolimits_{n} c_n \cdot \psi_n(x)
$$
Now i ...
-1
votes
0answers
44 views
TISE for hydrogen atom [closed]
I am given the radial component of the time independent Schrödinger equation for spherically symmetric electron wavefunctions: $$- \frac{\hbar^2}{2mr^2} \frac d {dr} \left(r^2 \frac {d \psi}{dr} \...
0
votes
1answer
28 views
Is it possible to reverse the spreading in space of a particle's wavefunction and if not, are all processes asymmetric in time?
Already more than a year ago, scientists claimed to have reversed the direction of time. What they actually did (see this article) to have reversed the direction of time. Which was hugely exaggerated. ...
0
votes
0answers
31 views
Energy spectrum for Linear potential [closed]
A particle in one dimension $(\infty<x<\infty)$ is subjected to a linear potential $\lambda x$ where $\lambda$ is a positive constant.
(a) Find the approximate expressions for energy ...
3
votes
3answers
107 views
Deriving the time-independent form of Schrödinger's equation
The motion of particles is governed by Schrödinger's equation,
$$\dfrac{-\hbar^2}{2m} \nabla^2 \Psi + V \Psi = i \hbar \dfrac{\partial{\Psi}}{\partial{t}},$$
where $m$ is the particle's mass, $V$ ...
1
vote
1answer
52 views
What is the meaning of Schrodinger equation solution for bound state of delta potential well?
Let's assume that we have delta potential well with $V = -\lambda\delta(x)$, where $\lambda >0$. Now if we solve Schrodinger equation, we get one eigenvalue $E_b=-\frac{m\lambda^2}{\hbar^2}$ with ...
2
votes
3answers
62 views
Confused about definition of three dimensional position operator in QM
My QM text defines the position operator as follows:
The position operator $X= (X_1,X_2,X_3)$ is such that for $j=1,2,3: \ X_j \psi(x,y,z)= x_j \psi(x,y,z)$.
To me this can mean two things.
1) $...
0
votes
3answers
78 views
Why are wavefunctions in Quantum Mechanics shown as complex Circular waves instead of real Planar waves?
I'm currently learning Quantum Mechanics from online video lectures and resources. In most of the web articles and videos, the wave functions are shown as circular waves $e^{i\omega t}$ instead of ...
0
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1answer
31 views
Time dependent perturbation, particle on a segment
Consider a particle of mass $M$ moving alongside a segment of length $a$.
Wavefunction:
$$\psi_n(x)=\sqrt\frac{2}{a} \sin(\frac{n\pi}{a}x)$$
Energy:
$$E_n=\frac{\hbar^2\pi^2 n^2}{2Ma^2}$$
Time-...
-2
votes
0answers
79 views
What really are eigenstates? [closed]
As far I've understood/misunderstood, there exists a State Vector in an infinite Hilbert Space. When an operator acts on an eigenstate it yields an eigenvalue times the eigenstate. What is the ...
3
votes
3answers
77 views
Where in experiment do you encounter Lorentizan wavefunction?
Is there an experimental system, or such that can be observed in nature where a particle's wave function assumes a form - $\psi(x)\propto \frac{1}{\sqrt{x^2+1}}$ such that $|\psi(x)|^2$ is Lorentzian?
...
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vote
2answers
34 views
On particle diffraction and its relation to the statistical interpretation of the wave function
Particles can be diffracted due to their quantum nature and that is understood by their wave-like behavior. Clearly seen in e.g. plane wave solutions of the Schrodinger equation or a superposition of ...
1
vote
1answer
28 views
Is orbital and wave function are same thing?
As we know that wave functions are the solution of schrodinger wave equation which contains all the information about an electron. We also tought that these wave functions are the atomic orbitals of ...
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0answers
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Do we get different Normalization constants when we solve for the Simple Harmonic Oscillator using the Analytic Approach and the Operator Approach? [closed]
I was trying to solve for $n=4$ of the Simple Harmonic Oscillator using the Analytic Approach and the Algebraic Approach (As Griffiths classifies it).
After following the standard procedure of ...
2
votes
1answer
35 views
Potential energy of particle in delta function potential
What is the potential energy of a particle in the single bound state $\psi_b(x)=\frac{\sqrt{m\alpha}}{\hbar}e^{-\frac{m\alpha}{\hbar^2}|x|}$ of the Dirac-delta potential well
$$V(x) = -\alpha \delta(x)...
1
vote
1answer
57 views
Inverse of Wave Reduction
Let's consider a system of three apparatuses. Sequentially these act as
A device that measures momentum of an electron
Parallel plates where electric field between them changes randomly.
Same device ...
0
votes
1answer
79 views
Quantum mechanically, is superposition a sum or a product?
This question may sound like a no-brainer, but I'm getting confused after watching this lecture (cf. the slide at minute 5:07).
The context is to motivate the quantization of a field which, for the ...
1
vote
2answers
73 views
About the physical definition of the Planck's constant
In Quantum Mechanics (QM), the Planck's constant has the S.I. units of
(energy) x (time). So, how should one interpret that?!
How should I understand the physical meaning of the following relations?
...
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0answers
23 views
Hellmann-Feynman theorem for nearly degenerate states
If we have:
$$\tag{1}
E(P)=\int \psi_a(P)^{*} H(P) \psi_b(P)\ \mathrm{d} \tau
$$
Then taking the derivative wrt. the parameter P yields:
$$
\begin{aligned} \frac{\mathrm{d} E}{\mathrm{d} P} &=\int\...
0
votes
1answer
47 views
“Probabilities are the ghosts of quantum mechanical amplitudes”
I came across this quote today;
[Quantum computers] process information using quantum mechanical amplitudes. And probabilities are sort of the ghosts of amplitudes after they have been degraded to ...
0
votes
1answer
35 views
Quantum mechanics - potential step problem
I've done potential steps where V > E0 and V < E0, but not where it's equal to 0. How would I go about answering this question? Any help is appreciated.
See below.
0
votes
1answer
81 views
Is the Hamiltonian fully defined by a quantum state (vector)? [duplicate]
From what I have read, the evolution of a quantum state is determined by the Hamiltonian (Schrodinger equation). However, I'm trying to understand if the Hamiltonian itself can be fully derived from ...
1
vote
2answers
70 views
Representation of wavefunction as superposition of eigenstates
In Quantum Physics it is postulated that, any general state $\psi$ can be represented as superposition of eigenstates with constant coefficients corresponding to any observable.
Say, I have all the ...
0
votes
1answer
123 views
The superposition principle in quantum mechanics
This is a question parallel to this question The importance of the phase in quantum mechanics.
In introductionary quantum mechanics I have always heared the mantra
The superposition principle ...
25
votes
8answers
2k views
The importance of the phase in quantum mechanics
In introductory quantum mechanics I have always heard the mantra
The phase of a wave function doesn't have physical meaning. So the states $| \psi \rangle$ and $\lambda|\psi \rangle$ with $|\lambda|...
0
votes
5answers
123 views
Zero Solution in infinite square well?
Consider the well:
$$V(x) = \begin{cases}
\infty&\text{if }x<0 \\
0&\text{if }x\in\left(0,L\right) \\
\infty&\text{if }x>L.
\end{cases}$$
Solving the time independent ...
5
votes
2answers
130 views
Wavelength as an observable in quantum mechanics?
Recently I was discussing a problem with one of my students in which she found that two states of the particle in a box were orthogonal and was then asked to give an example of an observable that ...
2
votes
3answers
179 views
Symmetrisation of (fermionic) two-particle system without vs. with spin in wave function
I'm using D. J. Griffiths's textbook Introduction to Quantum Mechanics (3rd ed.) for my introductory university course on the subject. In chapter 5 (starting at section 5.1.1), he discusses the ...
0
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3answers
81 views
Collapse of wavefunction to its eigenfunction upon measurement
In quantum mechanics, it is postulated that to every observable, we have an associated operator. It is further postulated that when we do a measurement on a system, the measured value is one of the ...
4
votes
2answers
747 views
Do the hydrogen atom's electron orbitals have Gaussian probability density functions?
In this article they show the following diagram:
Are all the diagrams in the little boxes really just Gaussian probability density functions with mean and variance (or covariance)? If not, what kind ...
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vote
0answers
51 views
Perturbation theory - integrals over different wavefunctions
I am reading a research paper on how to calculate g-tensors* computationally (Correlated four-component EPR g-tensors for doublet molecules).
In the theory section, they write "[...]from (quasi-)...
0
votes
1answer
20 views
TISE and uncertainty in energy
We use time independent schrodinger equation to find Stationary state solution for some potentials. My question is that, these Stationary state solutions are physically reliable or not? I am asking ...
1
vote
1answer
50 views
Annihilation operator acting on density operator in the position representation
I have a silly question.
I have a state $\hat{\rho}$ and I make the transformation $\hat{\rho}'=\hat{a}\hat{\rho}\hat{a}^\dagger$ (I want to subtract a photon).
I expand in the position basis the ...
-1
votes
1answer
79 views
Normalisation of the following wavefunction: $\psi(\theta,\phi)=\cos(\theta)$ [closed]
Normalisation of the following wavefunction:
$\psi(\theta,\phi)=\cos(\theta)$
So I thought about setting the following
$N\int \cos(\theta)\cos^*(\theta) d\theta=1$
But then maybe I thought I was ...
0
votes
1answer
33 views
Constructing solution to the time-dependent Schrödinger's equation
Given the initial state: $$\Psi(x,t=0)=c_1 \psi_1(x)+c_2\psi_2(x)+c_yy(x)$$ where $\psi_1$ and $\psi_2$ are eigenstates of $\hat{H}$ and $y(x)$ is a normalizable function but is not eigenstate of $\...
0
votes
3answers
30 views
Solving TISE for particle in the box for Infinite square well
While Solving the TISE for a particle an infinite square well with potential given by:
$$
U(x) = \left\{
\begin{array}{ll}
0 & \quad -L/2 \leq x \leq L/2 \\
\infty &...
0
votes
2answers
45 views
How to get effective quantum numbers of a linear combination of $\rm H$-atom wavefunctions?
The convention for the Hydrogen atom's interpretation subject to the laws of quantum mechanics is that you can prove the quantization of $|L|$, $L_z$, and Energy through quantum numbers $\ell$, $m_\...
3
votes
0answers
35 views
Radial wave function matrix elements
For hydrogen atom radial wave function is the analytic form of the matrix elements,
$$\langle n'\ell'|r^k|n\ell\rangle,$$
known? I am especially interested in $k=-2$ and $k=-3$.
Notation:
$$|n\ell\...
1
vote
2answers
44 views
Why does quantum tunneling increase de-broglie wavelength?
The picture (taken from a textbook) shows how quantum tunneling occurs with electrons.
Why does the de-Broglie wavelength of the electron change when doing this? It does not make intuitive sense to ...
1
vote
1answer
294 views
How to get the operator in Dirac bra-ket notation?
Suppose I have an operator given as $$T_a \psi(x) = \psi(x+a)$$ Is there a way I can get the operator in Dirac bra-ket notation. I am a newbie to QM. Please do give me hints.
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0answers
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Foliation of wavefunction
Is it meaningful to take different time slices (and other hypersurfaces) through a quantum wavefunction $\Psi$?
Below is a spacetime diagram, with axes $x$ and $t$. The wide band represents the ...
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votes
0answers
27 views
Expectation value of $p^2$ for an arbitrary real state function
I'm trying to obtain the expectation value of momentum squared for a real state function $(\Psi^*=\Psi)$.
I already know that
\begin{equation}
\left <p \right >=0
\end{equation}
for a real ...
1
vote
1answer
36 views
When does the wave function spread over the volume of a box?
I have heard colloquially that for any initial state, a particle enclosed in some volume $V$ will spread itself relatively evenly over that volume after large time, so that $|\psi(\vec{x})|^2\approx 1/...
3
votes
1answer
114 views
Integral kernel of the adjoint of operators
In the general case, the linear operator $\widehat{L}$ can be associated to a linear integral,
$$\Phi(\xi)\equiv\widehat{L}\Psi(\xi)=\int L(\xi,\xi')\Psi(\xi')d\xi',$$
where $L(\xi,\xi')$ is the ...
0
votes
1answer
34 views
Trouble understanding method used in the proof of Kinetic Energy operator is Hermitian
I am trying to understand why do we go from line 1 to line 2 in the way its shown? Why can't we directly just take the momentum operator squared outside and jump to line 3?
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votes
0answers
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How to choose boundary conditions for numerical solution of Schrodinger's equation whose solutions are expected to die out “at infinity”?
I am using the "Shooting method" for solving the TISE with a "reasonably arbitrary" potential in 1D,with boundary conditions such that the eigenfunctions $\psi_n\to0$ as $x\to\infty$(And another ...
0
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1answer
56 views
Why is the Laplace operator used in the Schrödinger equation? [closed]
Why is the Laplacian necessary in the time-dependent Schrödinger equation in a position basis for a non-relativistic particle?
$$i \hbar \frac{\partial \Psi}{\partial t} = -\frac{\hbar^2}{2m}\frac{\...
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votes
2answers
51 views
Discontinuous derivative of wavefunctions in the infinite square well potential problem?
I am intrigued about two points given in an answer to a similar question (https://physics.stackexchange.com/a/38198/262985).
On one hand, it is stated that wavefunctions inside the well (excluding ...
