I observe that all bound states have discrete energy levels, eg. particle in a box, hydrogen atoms. But unbound states always have a continuous energy spectrum. For example, for the case of a finite potential well, when ##E<V_0##, we have discrete energy for the bound states. When ##E>V_0##, the...
I am trying to solve the following exercise.
In a H atom the electron is in the state described by the wave function in spherical coordinates:
\psi (r, \theta, \phi) = e^{i \phi}e^{-(r/a)^2(1- \mu\ cos^2\ \theta)}
With a and \mu positive real parameters. Tell what are the possible values...
Using the boundary conditions where psi is 0, I found that k = n*pi/a, since sin(x) is zero when k*a = 0.
I set up my normalization integral as follows:
A^2 * integral from 0 to a of (((exp(ikx) - exp(-ikx))*(exp(-ikx) - exp(ikx)) dx) = 1
After simplifying, and accounting for the fact that...
Part a: Using the above equation. I got
$$\psi(x) = \int_{-\infty}^{\infty} \frac{Ne^{ikx}}{k^2 + \alpha^2}dk $$
So basically I needed to solve above integral to get the wave function. To solve it, I used Jordan's Lemma & Cauchy Residue Theorem.
And obtained $$\psi(x) = \frac {N \pi...
The answer is no and even when decoherence occurs for Wigner's Friend in the lab, quantum coherence remains. Let's start with the paper that illustrates this.
Assisted Macroscopic Quantumness
CONT.
https://arxiv.org/abs/1711.10498
Wow, I recently read this paper and the results are simply...
I have a basic question in elementary quantum mechanics:
Consider the Hamiltonian $$H = -\frac{\hbar^2}{2m}\partial^2_x - V_0 \delta(x),$$ where ##\delta(x)## is the Dirac function. The eigen wave functions can have an odd or even parity under inversion. Amongst the even-parity wave functions...
If you look at the recent Wigner's Friend experiment, it seems to support Carlo Rovelli's Relational Interpretation which says there's no real measurement.
Wiger's Friend carries out a polarization measurement. Before he does, the quantum system is in a superposition of horizontal/vertical...
This is what I have so far: $$ |\alpha\Psi_1 + \beta\Psi_2|^2 = |\alpha|^2|\Psi_1|^2 + |\beta|^2|\Psi_2|^2 + \alpha^*\beta\Psi_1^*\Psi_2 + \alpha\beta^*\Psi_1\Psi_2^* $$
$$=> |\alpha\Psi_1 + \beta\Psi_2|^2 = |\alpha|^2|\Psi_1|^2 + |\beta|^2|\Psi_2|^2 + 2Re(\alpha^*\beta\Psi_1^*\Psi_2) $$
I am...
Suppose one measures the position of a photon without destroying it. From my understanding, the wavefunction of the photon should collapse, and will return to a more spread out state over time. How would one calculate this, specifically the rate at which the wavefunction spreads out from the center?
We are given the wave function with spin, but it doesn't say in which Ylm each spin X± goes. So how do I know?
Examples;
(1) Ψ = 1/√3 R21(r) ( Y10
√2Y11 )
Here we have the up Spin X+ to Y10 and the X- to Y11
I notice the X- went to...
In https://en.wikipedia.org/wiki/Lamb_shift about the lamb shift, it's mentioned that the change in the electron's frequency due to QED effects (vacuum polarization and self-energy correction) is about 1 GHz, which would translate to an energy change of hf = 6.63E-25 J. This is 3E-7 times of the...
Suppose that the spacetime is discrete, with only certain positions being possible for any particle. In this case, the probability distributions of particles have nonzero values at the points on which the wavefunction is defined. Do we need randomness in the transitions of particles in such a...
Considering the quantum mechanical model for an atom, what exactly happens when two atoms (say, two Ca2+ ions in a Brownian motion) collide with each other? As I know, this collision is not like a regular elastic or inelastic collision between two macroscopic objects. Is it mainly due to the...
In https://arxiv.org/pdf/quant-ph/0203049.pdf, which is in the realm of Bohmian mechanics, Antony Valentini claims that by having a "non-equilibrium" particle with arbitrarily accurate "known" position, we can measure another particle's position with arbitrary precision, violating Heisenberg's...
Look at the paper in the link below:
https://link.springer.com/content/pdf/10.1007%2Fs10701-016-0026-7.pdf
It introduces a pilot-wave model on a discrete spacetime lattice. However, the pilot-wave model is not deterministic; the motion of quantum particles is described by a |Ψ|^2-distributed...
A free electron, or any other quantum particle, has an uncertain position/momentum, according to Heisenberg uncertainty principle. The squared amplitude of the wavefunction determines the probability of finding the electron at any point of the space. Accordingly, atomic orbitals are attributed...
I have question, how can I solve problem of particle in rigid box when one of the wall gets completely destroyed? At time t = 0 the right wall of box gets completely destroyed, left wall is still here( ψ(0) = 0 ), also at t = 0 we know that particle is in ground state.
How can I search for...
In https://www.sciencedirect.com/science/article/pii/S0378437109010401, the author claims that the interference pattern obtained in the double-slit experiment does not need a wave description of matter, and can be accounted for by the "quantized momentum transfer" from the slits to the electron...
Homework Statement
Consider the state
$$\psi_\alpha = Ne^{\alpha \hat a^\dagger}\phi_0, $$
where ##\alpha## can be complex, and ##N = e^{-\frac{1}{2}|\alpha|^2}## normalizes ##\psi_\alpha##.
Find ##\hat N \psi_\alpha##.
Homework Equations
$$\hat N = \hat a^\dagger \hat a$$
$$\hat a\phi_n =...
Hi,
I'm sorry if this question has already been answered somewhere and I'm just too incompetent to find it, buuut:
As the title already says, I really do not get that part of quantum physics (if you can even say I'm getting ANY part at all...).
As I searched all Google for an answer I just...
Homework Statement
A particle of mass m in one dimension has a potential:
$$V(x) =
\begin{cases}
V_0 & x > 0 \\
0 & x \leq 0
\end{cases}
$$
Find ##\psi(x)## for energies ##0 < E < V_0##, with parameters
$$k^2 = \frac{2mE}{\hbar^2}$$
and
$$\kappa^2 = \frac{2m(V_0 - E)}{\hbar^2}$$...
Homework Statement
How should I calculate the expectation value of momentum of an electron in the ground state in hydrogen atom.
Homework Equations
The Attempt at a Solution
I am trying to apply the p operator i.e. ##-ihd/dx## over ##\psi##. and integrating it from 0 to infinity. The answer I...
...to give a number?
https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2016/lecture-notes/MIT8_04S16_LecNotes5.pdf
On page 6, it says,
"
Matrix mechanics, was worked out in 1925 by Werner Heisenberg and clarified by Max Born and Pascual Jordan. Note that, if we were to write xˆ...
I need to know what is the typical extention of the (spatial) wavefunction of an atomic nucleus in a crystal, in particular I am interested to the case of a Germanium cristal.
Please together with the actual number of the size of the nuclei wavefunctions, let me know the references (articles or...
Homework Statement
The Attempt at a Solution
[/B]
Hi All,
I'm having trouble answering part (f) of the above question. I have managed parts (d) and (e) fine but am not sure how to proceed with part (f). I am pretty sure that the amplitude of the reflected wave in region 1 will be zero...
If I understand it correctly, a particle doesn't have a definite momentum and a definite position, but is in a superposition of multiple positions and momenta. And when we measure either of the two quantities, say, position, the wavefunction collapses to tell us where the particle is. Now when...
For the harmonic oscillator, I'm trying to study qualitative plots of the wave function from the one-dimensional time independent schrodinger equation:
\frac{d^2 \psi(x)}{dx^2} = [V(x) - E] \psi(x)
If you look at the attached image, you'll find a plot of the first energy eigenfunction for...
In ab initio calculations for periodic systems, only an irreducible K grid is used for calculation, and consequently only those K points have their wavefunction calculated. My question is, how to recover wavefunction at other K points not included in the irreducible K grid? Similar questions to...
Hi physicsforums,
I am an undergrad currently taking an upper-division course in Quantum Mechanics and we have begun studying L^2 space, state vectors, bra-ket notation, and operators, etc.
I have a few questions about the relationship between L^2, the space of square-integrable complex-valued...
Hi, are there any models known in QM where the wavefunctions do not have to be infinitely differentiable, and thus can exist in other spaces than the Hilbert space? I assume Banach spaces allow elements that are not infinitely differentiable as subsets. Can therefore certain phenomena in QM be...