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.
2,668
questions
2
votes
1answer
19 views
Problem Regarding Quantization in Goodstein's Book
This question regards what is stated at page 65, Goodstein, States of Matter.
We want to consider a free particle in one dimension, with movements restricted to a line of lenght $L$; so in practice we ...
0
votes
0answers
31 views
Is there an equivalence between the creation of a wavefunction and the collapse of a wavefunction?
I am thinking here of how creation vs. absorbtion compare for a photon. A single photon may be emitted when an electron in an atom returns down to the ground state from an excited state. In a ...
2
votes
0answers
21 views
Probability of two electrons of different energy levels contained in a single infinite potential well being found in same region
What is the probability of two electrons in a single infinite potential well centered at 0, one in the ground state, the other in the first excited state, being in the same region?
I know by the Pauli ...
0
votes
1answer
48 views
Normalization of a wavefuntion [closed]
I am working with the following wavefuntion which describes two entangled photons. I need to normalize it.
\begin{equation}
\Phi(\omega_\alpha,\omega_\beta)= \frac{1}{\omega_\alpha-1+0.5i}\frac{1}{...
0
votes
1answer
54 views
Wave function and speed of light
When a photon is generated, it travels at the speed of c in the form of propagating electromagnetic wave until the photon interacts with something else to have its energy absorbed or converted. Is ...
-2
votes
1answer
85 views
Origin of probabilities in Quantum Mechanics?
The non-normalized wavefunction of a general qubit is given by:
$$|\psi\rangle=A|0\rangle+B|1\rangle.$$
The complex amplitudes $A$ and $B$ can be represented by two arrows in the complex plane:
Now ...
2
votes
1answer
70 views
Why must systems of identical particles be either totally antisymmetric or totally symmetric? Why can there not exist a mixture?
I am reading chapter 6 of Sakurai's Modern Quantum Mechanics and have come across the 'symmetrization postulate', which tells me that for any given system of identical particles, all states must ...
0
votes
2answers
45 views
How does the electron understand that it being observed in the double slit experiment?
I was reading about the double slit experiment that proved the wave and particle nature of electron. I read that electrons give a diffraction pattern when they are not observed (wave nature) and ...
1
vote
1answer
47 views
Problems deriving the Quantum Hamilton-Jacobi equation
This is my first question at Physics SE so please be kind. I am well versed in the etiquette over at Math SE, but not so much here. Anyway, I thought this question was better suited to this site ...
0
votes
1answer
51 views
Matrix elements of operators in position representation
In a lecture note, it is written
$$
T_{ij} = \langle \phi_i| \hat{T} | \phi_j \rangle
= \int d^3 \vec{r} \phi_i^*(\vec{r}) T(\vec{r}) \phi_j(\vec{r})
$$
How to obtain the second integral form from ...
0
votes
0answers
39 views
Do “functions” always refer to “wavefunctions” in quantum mechanics?
For example, what do we mean when we say that “Operator acts on the function that follows it”? What are the examples of “functions” that operators act on (in quantum mechanics)?
0
votes
0answers
30 views
Infinite linear potential well?
I am currently learning and solving Schrodinger's time independent equation for particles under various 1D-potentials.
Would it be possible to have a mix of a linear potential (of the form $U(x)=Fx$ ...
2
votes
1answer
103 views
Why is the first derivative of the time-dependent Schrödinger equation continuous? Where does it come from?
I was taught in first year physics that the first derivative of the time-dependent Schrödinger equation had to be continuous. However I was never taught (or at least I don't remember) the reason why.
\...
2
votes
4answers
88 views
Is there interferences between 2 electron wavefunctions?
The 2 slits experiment done with 1 electron shows interference from the "splitted" wavefunctions.
My question is, if we sent 2 electrons simultaneously in the 2 slits and each one can go in ...
2
votes
2answers
86 views
What is the physical justification for the boundary conditions of the Schrödinger equation for an infinite potential well?
All the literature says that the physically meaningful solutions to the Schrödinger equation in an infinite potential well must fulfill the boundary condition that the wave function is $0$ at the ...
0
votes
2answers
45 views
Is the complex conjugate of the amplitude of an electron wavefunction equivalent to the amplitude of the corresponding hole?
Is the complex conjugate of the amplitude of an electron wavefunction equivalent to the amplitude of the corresponding hole? Say I consider a wavefunction of an electron that has the amplitude A. If I ...
0
votes
1answer
39 views
Wave functions in different pictures of quantum mechanics [closed]
In quantum mechanics both Heisenberg picture and Dirac picture has same expression for wave function then why wave function of Dirac picture is considered time dependent while Heisenberg picture has ...
2
votes
1answer
90 views
Fourier transform of a real initial wavefunction
Consider the initial wavefunction given by:
$$ \Psi (x,0) = \sin(k_0 x).$$
I've been taught that in order to time evolve a wavepacket one must first find the momentum space representation of the ...
0
votes
4answers
105 views
Are there experiments that show that the electron wave function can be point-like? [closed]
I know that there are scattering experiments that show that electrons act like structureless particles up to extremely small scales. But in these experiments the electrons are moving, so their wave ...
0
votes
3answers
78 views
Why does the wavefunction of a particle spread out after a measurement?
Quantum mechanics states that the wave packet of a particle "spreads-out" in position again after a measurement on this particle has been made. Is this spreading or "dispersion" ...
3
votes
1answer
35 views
How do I normalize the relativistic wavefunction in general?
https://en.wikipedia.org/wiki/Spacetime_algebra#Relativistic_quantum_mechanics claims that the wave-function can be written using geometric algebra as follows:
$$
\psi=R(\rho e^{i\beta})^{1/2}
$$
...
-1
votes
0answers
30 views
Can sequential measurements on a particle yield different results?
Suppose the spin of a non-interacting quantum particle is measured "spin up" on the $z$-axis. After the measurement the wavefunction of the particle spreads out again and returns to a ...
0
votes
0answers
42 views
Is there a limit of wave function splitting?
It is possible to split the wave function (for example using a semi mirror like in Wheeler delayed choice experiment). I wonder what happens if we split it many times.
My "though experiment" ...
0
votes
0answers
25 views
Measurement of non well-defined magnitudes (position)
Lets consider an hydrogen atom (superposed states) and the mesurement of it's angular momentum ($\hat{L_{z}}$, in this case) since at least is defined. I imagine the mesurement could be something like ...
0
votes
0answers
37 views
Relating the Minev et al experiment to Brun QTT survey
I have been studying from many angles the groundbreaking/now renowned Minev et al experiment: To catch and reverse a quantum jump mid-flight [1]. I have many questions on this complex/intricate setup ...
8
votes
5answers
1k views
What are the necessary and sufficient conditions for a wavefunction to be physically possible?
Often times it is stated in books that a quantum state is physically realizable only if it is square integrable. For example in Griffiths (2018 edition) page 14 he stated
Physically realizable states ...
5
votes
2answers
147 views
Hilbert space in Dirac's representation
I've been reading some old posts here on physics stack exchange and I realized something that have never ocurred to me before.
Let $\mathscr{H}$ be a Hilbert space over $\mathbb{C}$. An orthonormal ...
3
votes
2answers
147 views
Correct interpretation of $\langle x | \psi \rangle$?
Suppose $|x\rangle$ is an eigenvector of the position operator $\hat{x}$ and let $|\psi\rangle$ be an arbitrary state on this Hilbert space. What is the correct interpretation of the complex number $\...
1
vote
3answers
130 views
What is the significance of a Hilbert space? [closed]
I see the term Hilbert space thrown around a lot. At first I thought it is just when you have complex vectors and define an inner product between them. However, it seems to be a lot more than that ...
0
votes
1answer
43 views
Time dependent wave function of a particle in a gravitational field
I found this great question about the solution of the Schrodinger equation for a particle in a constant gravitational field, but the solution they wanted is to the time independent Schrodinger ...
0
votes
1answer
74 views
$V(x)=V_0\sin^2(k_0x) $ potential, 1 dimensional [closed]
If I have a potential like this:
$$V(x)=V_0\sin^2(k_0x) $$ where $k_0^2=2m/h^2E_*$
how can I prove that the wavefunctions are:
$\Psi_q(x)=e^{iqx}u_q(x)$ where $qe[-k_0,k_0]$ and $u_q(x)$ is periodic
...
5
votes
6answers
729 views
Is a wave function a ket?
I just started with Dirac notation, and I am a bit clueless to say the least. I can see Schrödinger's equation is given in terms of kets. Would I be correct to assume if I were given a wavefunction, ...
3
votes
4answers
131 views
Why does the antibonding orbital has higher energy (than the bonding orbital) if the Coulomb repulsion is lesser?
Depending on its strength, the attractive double dirac delta potential shown below
can support two bound states. They are called the bonding and the antibonding orbitals as shown in the figure below
...
0
votes
1answer
33 views
Set of probabilities distributions inside a infinite square well [duplicate]
Its been some years since I did the infinite square well. I am doing an econimics problems with probability distributions and I vaguly remember there being a name for either the wave functions in the ...
-3
votes
1answer
46 views
What's $k$ in the wave equation (Quantum Tunneling)? [closed]
Given the wave function $\psi(x)= A_1\,e^{i\,k\,x} + A_2\,e^{-i\,k\,x}$ that describes a wave being transmitted and reflected on a potential barrier. In this context I find different notations for $k$:...
0
votes
2answers
76 views
Why use a path integral if we have a general solution to the Schrödinger equation? [closed]
In this answer, the general solution to the Schrödinger equation is given, and is also included here. In my QM class we talk a lot about this equation, but we haven't seen path integrals yet, and I ...
1
vote
1answer
35 views
Normalisation of wavefunction given by the form $Ae^{i(kx-wt)}$
Question 1.
Let's say that the wavefunction is given in the form
$$\Psi(x, t) = Ae^{i(kx-wt)}$$
Then because of the normalisation condition, the following should hold.
$$\int \Psi^*\Psi dx = A^2 \int_{...
0
votes
0answers
54 views
Proof bound states exist on vanishing, negative potentials in 1D
I want to prove the following:
Show that for any one dimensional, time independent potential $U(x)$, where $\lim\limits_{x \rightarrow \infty}{U(x)} = 0$ and $\int_{-\infty}^{\infty}U(x) < 0$ ...
0
votes
1answer
37 views
One-body operator for fermions - equality
I am reading Modern Many-Particle Physics by Lipparini. In chapter 1.5 he talks about the matrix elements of the one-body operator:
$$F_1 = \sum_{i=1}^{N}f(x_i)$$
He mentions that the matrix elements ...
0
votes
1answer
45 views
Can we make a symmetric wavefunction out of two anti-symmetric wavefunctions?
And, if so, then can be say that we've made a boson out of two fermions?
Mathematically,
If
f=fermion=f(x,y)
then
b=boson=[f(x,y)-f(y,x)]/2
0
votes
1answer
15 views
What happens to a function generator waveform when another capacitor is added in parallel with an existing capacitor in a circuit?
I am trying to gain an understanding of the first-order response of RC circuits and measurement of capacitance in a capacitive sensor using function generation and oscilloscopes. I had a question ...
1
vote
0answers
29 views
Proper way of adding parameters to a test wave function
So experimenting with the variational method, I thought of a test wave function for an infinite deep well system,
$$\Psi(x) = N(a^2-x^2) \text{ for $-a$ < $x$ < $a$}$$
and $0$ everywhere else.
...
0
votes
1answer
31 views
Eigen-energy in Finite Quantum Well
So I'm a beginner at quantum mechanics and I'm learning about finite quantum wells. I've been stuck on an example on how to find Eigen-energies in conduction and valence bands of the quantum well ...
1
vote
0answers
28 views
Energy Levels in Double Finite Well potentials [closed]
Why is there a behaviour where $E_1$ and $E_2$ are close to each other? This question is already answered before but I did not understand the explanation about symmetric and asymmetric terms as I do ...
0
votes
0answers
16 views
Condition for a trial wavefunction to determine whether or not it will lead to bonding in an ion
Suppose we have some ion such as $H_2^+$ and we produce some trial electronic wavefunction. For example, we take the simple trial wavefunction made up of a single 1s orbital of the hydrogen atom ...
0
votes
1answer
98 views
Orthonormality condition in quantum mechanics [closed]
What does the orthonormality condition in quantum mechanics truly signify? Does it have a physical meaning? Or is it just a method of normalization applied in order to find the probabilities?
0
votes
1answer
58 views
Showing that two wavefunctions are orthogonal [closed]
I have two function:
$\Psi_A(x,0)=\sqrt{\frac{1}{6}}\phi_0(x)+\sqrt{\frac{1}{3}}\phi_1(x)+\sqrt{\frac{1}{2}}\phi_2(x)$
$\Psi_C(x,0)=\sqrt{\frac{3}{8}}\phi_0(x)+\sqrt{\frac{5}{8}}\phi_2(x)$
I have to ...
0
votes
1answer
79 views
How precisely can particle position be measured in a laboratory?
If we have any given particle, such as a photon or an electron (it doesn't really matter what for the sake of the question), how precisely can modern physics devices measure their position? ...
1
vote
1answer
73 views
What is the specific Hilbert space of the finite square well?
For a free particle, the QM Hilbert space is $L^2(-\infty,\infty)$ which is the space of all square integrable functions. As a result, this space does not contain functions of the form $e^{\alpha x}$ ...
1
vote
1answer
72 views
How are linear combination of energy eigenstates solutions to the TISE?
My textbook states that:
TISE is a generic eigenvalue problem and the superposition state is not a solution to the TISE.
Another part of textbook (in context of infinite square well):
The most ...
