I'm trying to understand how quantum systems behave when they are perturbed, and I'm using the quantum harmonic oscillator as a model.
I start by implementing a symmetric gaussian shaped bump in the middle of the harmonic oscillator, and then i propagate the wave functions in time.
the...
In solid state physics or statistical physics, the many-body spin Hamiltonian is written as ##\sum_{i,j} \hat{S}_{i}\cdot \hat{S}_j##. I referred to many textbooks, and most of them just generalised this from the two-electron case ##\hat{S}_{1}\cdot \hat{S}_2##. While this seems natural, it is...
In the 1934 novel by John Taine, Before the Dawn, scientists are able to retrieve images of the past by accessing the light absorbed by stones throughout history. While this is fictional, 1934 was really before the dawn of quantum physics.
In the far future, could we retrieve images from light...
When two slits produce an interference pattern, and one slit is closed, then the interference pattern disappears. But one slit interference should still be possible. What should be the measurements of each slit for this to occur? That is, that, starting with a double slit, closing one slit does...
Hi, this was one of the oral exam questions my teacher asked so i tried to solve it. Consider y>0 the energy spectrum here is continuous and non degenerate while for y<0 the spectrum is discrete and non degenerate because E<0.
for y>0 i thought of 2 cases
case 1 there is no wave function for...
I would really appreciate some help with a question I have aboute the TISE (Sch. tipe indipendent equation). This is a linear equation and linear combination of the solution should be solution too. The problem is that for the free particle, which solution can be written like exp[-ikx], a linear...
Hi everyone,
I need some help getting the gist of Bell’s theorem and his notion of inequalities.
How would you explain it to someone with limited knowledge of mathematics?
What are the potential implications?
I am wondering why the photon is necessary at all. Is there experimental evidence of its existence? My understanding is that it experiences no time or distance. So if this is true why do we need it at all? Why not just say that a particle here interacts with a particle there. Do we use the...
Hello! I have some questions regarding the photon emission and whether the atom recoils or not.
When an electron in an atom emits a photon. One can calculate the energy of the photon by the difference between the energy levels from where it left to which it returned.
Let’s say it jumped from...
Apart from the usual integral method, are there any other ways to find expectation value of momentum? I know one way is by using ehrenfest theorem, relating it time derivative of expectation value of position operator.
Even using the uncertainty principle, we might get it if we know the...
In classical electromagnetism I think I have understood the following(please correct me if something is wrong): A charge produces an electric field, a charge moving with constant velocity produces a magnetic field, an accelerating charge emits electromagnetic radiation. In radio antennas this is...
Zero spin of Higgs boson? Is it really zero? Where is the spin (intrinsic angular momentum) of the Higgs boson on so small that we quantify it as having zero spin?I am aware of the reduced plank constant. But I we sure there is nothing in between the reduce Planck’s constant and the zero spin of...
Hi! My name's Logan Knox and I'm aspiring to eventually understand the physics and nature of the quantum world in its totality, and I have a LONG way to go, but I have to get there by asking the right questions, and I think this is the first step to finding the right question to ask for this...
I studied at UBC, U of Leiden, in quantum statistical mechanics and kinetic theory. I worked in chemistry at McGill University for many years doing the theory of NMR which involves spin theory. In 1997 I gave up NMR and started to study the EPR paradox. I do not follow the party line because I...
I've been reading about Quantum Mechanics for years now and I think it's time I bought a textbook and really learned the math. I'm 15 y.o. and have a working understanding of Derivitives, Integrals and Vectors. Is this textbook a good one to start with or is it too complex? Which one would you...
Hello fellow physicists,
I need to calculate the rotational partition function for a CO2 molecule. I'm running into problems because I've found examples were they say this rotational partition function is:
##\zeta^r= \frac T {\sigma \theta_r} = \frac {2IkT} {\sigma \hbar^3}##
Where...
So let's say that we have som unitary matrix, ##S##. Let that unitary matrix be the scattering matrix in quantum mechanics or the "S-matrix".
Now we all know that it can be defined in the following way:
$$\psi(x) = Ae^{ipx} + Be^{-ipx}, x<<0$$ and $$ \psi(x) = Ce^{ipx} + De^{-ipx}$$.
Now, A and...
Practically it is said that, given two spin states |u⟩ (up) and |d⟩ (down) - which are the spin measured along the +z and -z semiaxes - such that they are orthogonal ( ⟨u|d⟩ = ⟨d|u⟩ = 0), it is possible to write any other spin states using a linear combination of these two (because they are a...
I am unable to complete the first part of the question. After I plug in the function for psi into the differential equation I am stuck:
$$\frac {d \psi (r)}{dr} = -\frac 1 a_0 \psi (r), \frac d{dr} \biggl(r^2 \frac {d\psi (r)}{dr} \biggr) = -\frac 1 {a_0}\frac d {dr} \bigl[r^2 \psi(r) \bigr] =...
I started and successfully showed that the expectation of X_1 and X_2 are zero. However the expectation value of X1^2 and X2^2 which I am getting is <X1^2> = 0.25 + \alpha^2 and <X2^2> = 0.25.
How do I derive the given equations?
The difference between light and very heavy atoms reflects itself in these two schemes.
My question is why one scheme for the vector sum is necessarily the right & suitable sum model for one case, and the 2nd scheme suits the 2nd case ?
In other words, why & how the relative magnitude of the...
I want to exactly diagonalize the following Hamiltonian for ##10## number of sites and ##5## number of spinless fermions
$$H = -t\sum_i^{L-1} \big[c_i^\dagger c_{i+1} - c_i c_{i+1}^\dagger\big] + V\sum_i^{L-1} n_i n_{i+1}$$
here ##L## is total number of sites, creation (##c^\dagger##) and...
Dirac wanted to fix the problems with the Klein-Gordon equation by seeking a new solution to it.
He wanted a relativistic solution so it makes sense that the solution needed to satisfy Einstein's energy-momentum relation.
But why did it need to be of first order in time- and...
In the last paragraph of these notes, https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2016/lecture-notes/MIT8_04S16_LecNotes3.pdf, it says how a state with large number of photons is not classical. Why is that? I thought quantum mechanics' laws were most applicable when we...
In everyday language, beauty is an emotional concept. How would you mix that with quantum physics and the mathematics behind it? Or is what he refers to as "beauty" is more like simplicity? I mean, I agree with the man, the Standard Model feels redundantly complex, but I feel like there is...
I'm currently in my first QM course and we have griffiths as our textbook. Although Griffiths is a great read I'm having trouble really conceptualizing QM ideas. We've only covered infinite potential well and wave packets as of now. Are there any additional resources or textbooks in which they...
Homework Statement
Homework EquationsThe Attempt at a Solution
Hi All,
My problem is that when I calculate this integral or use software to do it for me I get (3*i*pi)/16, when I've been told that the answer is 1/2i giving a probability of 1/4. Would someone be able to point out where my...
If we have a particle, say, an electron and we shoot it straight through an empty box. This box is surrounded by light sources on its two sides:
So, if you consider the above cube, if we shoot a particle in a straight line such that it crosses the face ABEF and it crosses the face HGDC through...
Hello,
can anybody help me with solving the problem.
Homework Statement :[/B]
Calculate minimum uncertainty?
A horizontal beam of laser light of wavelength 604 nm passes through a narrow slit that has width 0.0600 mm . The intensity of the light is measured on a vertical screen that is 2.40...
Hello everyone, I'm an Undergrad and I'm trying to set the Quantum key distribution experiment by using weak laser pulses(the laser diode with attenuated filter). but I don't know how to calculate the photon number per pulse. Can anyone tell me how to calculate the photon number per pulse...
Homework Statement
I am supposed to construct a controlled Hadamard gate
using only single qubit and CNOT gates.
Homework Equations
[/B]
We know that any arbitrary unitary Operator U can be written as the Martrix product U=AXBXC, where X is the NOT-Matrix and ABC=1 (identity matrix)
I've...
Given that position and momentum are Fourier conjugates, what is the derivation for the equation ##\hbar \vec{k} = m \vec{v}##, where momentum-space momentum is defined as ##\hbar \vec{k}## and position-space momentum is defined as ##m \vec{v}##?
Dear All,
I have a couple questions on the double slit experiment I hope you can help shed some light (or photons) on. =)
Arrival Timing of Photons
In a normal double-slit experiment like the above setup, do photons always arrive at the detector at a constant speed (basically, speed of light)...
Homework Statement
Consider Compton scattering of a photon by a moving electron. Before the collision
the photon has wavelength λ and is moving in the +x-direction, and the electron is
moving in the −x-direction with total energy E (including its rest energy mc2). The
photon and the electron...
https://en.wikipedia.org/wiki/Future_of_an_expanding_universe "Over an infinite time there could be a spontaneous entropy decrease, by a Poincaré recurrence or through thermal fluctuations (see also fluctuation theorem)"
Homework Statement
I have ##H'=ax^3+bx^4##, and wish to find the general perturbed wave-functions.
Homework Equations
First-order correction to the wave-function is given by, $$\psi_n^{(1)}=\Sigma_{m\neq n}\frac{\langle\psi_m^{(0)}|H'|\psi_n^{(0)}\rangle}{n-m}|\psi_m^{(0)}\rangle.$$
The...
Homework Statement
Simple question we have to answer:
(Physics) How do I release the electrons from the cathode with a color filter? (The so called
Photoelectric effect)Homework Equations
none
The Attempt at a Solution[/B]
Here we have a conflict , the so called wave-particle duality, if...
Hey, I've being studying the Photoelectric effect, I think I understand it superficially. One thing that has been bugging me is this:
"Given that it is possible to move electrons with light and given that the energy in a beam of light is related to its intensity, classical physics would predict...
It seems to me that we don't measure a particle because a particle doesn't have an objective existence independent of the wave function or does it? The wave function in this case would have to be real because you can't have probability without the underlying possibility of a specific outcome...
Given:
##\textbf{E}=\hbar \textbf{k}##
where ##\textbf{k} = [\vec{k}_1, \vec{k}_2,\vec{k}_3, i c \omega]##
If ##\textbf{k}## can vary continuously, how does the equation imply that energy is quantized?
For example, ##y = m x +b## where ##m = \hbar## does not imply quantized ##y##.
For...
In a lecture from a course in QM, it was mentioned that Shroedinger's equation is deterministic in one and two dimensions. But in third dimension it gives unstable solutions, loosing it's determinism.
It was mentioned that "in space of D dimensions Gauss theorem leads to the conclusion that...
I am still in secondary school so I probably shouldn't think about things this complicated (at least that's what it seems to me, complicated), but please correct me if I'm wrong. If I recall correctly, the position of an electron is never certain, and always based on probability, unless...
Can any expert help me in explaining how this example below get the reduced density matrix from the density matrix in bipartite system.
$$\rho =\frac{1}{4}\begin{pmatrix} 1 & 1 & cos(\frac{\alpha}{2})-sin(\frac{\alpha}{2}) & cos(\frac{\alpha}{2})+sin(\frac{\alpha}{2}) \\ 1 & 1 &...
Homework Statement
A beam of electrons with kinetic energy 50 eV is fired at a 100 nm thick crystalline nickel foil.
(a) Calculate the speed of the electrons in the beam.(b) Based on your answer to part (a), state, with justification, whether classical (Newtonian) mechanics correctly...