States Definition and 1000 Threads

Homework Statement Consider a potential function V(x) such that: $$ \begin{cases} V(x)\leq 0\text{ for }x\in[-x_0,x_0] \\ V(x)=0 \text{ for }x\not\in[-x_0,x_0] \end{cases} $$ Show, using the variational method that: (a) In the 1-dimensional case \lambda^2V(x) always possesses at...

Homework Statement A particle is confined to a two-dimensional box defined by the following boundary conditions: U(x, y) = 0 for \frac{-L}{2} ≤ x ≤ \frac{L}{2} and \frac{-3L}{2} ≤ y ≤ \frac{3L}{2}, and U(x, y) = ∞ outside these ranges. Determine the energies of the three lowest energy states...

Homework Statement Hey dudes So here's the question: Consider the first excited Hydrogen atom eigenstate eigenstate \psi_{2,1,1}=R_{2,1}(r)Y_{11}(\theta, \phi) with Y_{11}≈e^{i\phi}sin(\theta). You may assume that Y_{11} is correctly normalized. (a)Show that \psi_{2,1,1} is orthogonal...

Homework Statement Find the density of states g(ε) for an ideal quantum gas of spinless particles in dimension d with dispersion relation  ε= α|p|s , where ε is the energy and p is the momentum of a particle. The gas is confined to a large box of side L (so V = Ld) with periodic boundary...

Homework Statement The wave function for a system of two hydrogen atoms can be described approximately in terms of hydrogen wave functions. (a) Give the complete wave functions for the lowest states of the system for singlet and triplet spin configurations. Sketch the spatial part of each...

what do you mean by density of states ? can you please explain to it ?

I'm wondering what the name of a switch that alternates between two states only when depressed. An example would be a flashlight, where if you click it once, it turns on, and if you click it off, it turns off (no need to hold down the button to get a continuous light).

I've always taken this for granted. Now I am looking for an answer. When electron jumps from a higher orbit to lower orbit it releases energy. Why is the energy in the form of photon? I will take another example which will make my question easy to understand. When two electrons are kept...

Homework Statement A system is made of N 1D simple harmonic oscillators. Show that the number of states with total energy E is given by \Omega(E) = \frac{(M+N-1)!}{(M!)(N-1)!} Homework Equations Each particle has energy ε = \overline{h}\omega(n + \frac{1}{2}), n = 0, 1 Total energy is...

Is there a way to write p1 |v1> + p2 |v2> if it is not a pure state but a mixture? thanks.

Hi, Here I have a question, apparently easy, but that I think it is a bit tricky. Homework Statement Indicate how can a hydrogen atom be prepared in the pure states corresponding to the state vectors ψ2p-1 and ψ2px and ψ2s. It is assumed that spin-related observables are not...

What are the differences between the triplet and singlet states. triplet state-- parallel spins-- S=1 , 2S+1=3 Singlet state-- Paired spins---S=0 , 2S=1= 1 singlet state has paired spins of electrons in the same orbit, thus there are repulsion force between the two electron in the same...

Hello everybody, I have a question which might be silly. Nevertheless: Can exited states exist if you know that the ground state do not exist? Will in such a case first exited state become the ground state? Thanks.

Homework Statement What is the expectation value of \hat{S}_{x} with respect to the state \chi = \begin{pmatrix} 1\\ 0 \end{pmatrix}? \hat{S}_{x} = \frac{\bar{h}}{2}\begin{pmatrix} 0&1\\ 1&0 \end{pmatrix}Homework Equations <\hat{S}_{x}> = ∫^{\infty}_{-\infty}(\chi^{T})^{*}\hat{S}_{x}\chi...

Homework Statement An atom in an excited state has a lifetime of 1.2 x 10 -8 sec; in a second excited state the lifetime is 2.3 x 10 -8 sec. What is the uncertainty in energy for the photon emitted when an electron makes a transition between these two levels? Homework Equations...

Forgive me as I have no formal secondary education so my actual knowledge of terms and what not is limited but I am working on a theory that has me wanting to explore the varying chemical states of matter and what defines them. For example, how Nitrogen can be both a gas and a liquid in room...

Hi guys, Just a quick question, is the following statement true (it seems to be implied in the article I'm looking at); Ʃ(|α|2)n = 1 (The sum over n=0 to infinity) Thanks to anyone who takes a look.

Do protons and neutrons have excited states? This page shows some simulated shapes of protons. http://discovermagazine.com/2003/aug/breakprotons Do the different shapes have to do with different energy states of the proton?

Hi folks -- quick question. I appreciate that entangled states in quantum mechanics may not be bound states. But when we have bound states, are the particles always entangled with one another? Thanks a lot!

For a free electron gas the procedure for determining the density of states is as follows. Apply periodic boundary conditions to the free electron waves over a cube of side L. This gives us that there is one state per volume 2\pi/L3=2\pi/V And from there we can find the number of states at a...

In the double delta function potential well, where one delta function ( -αδ(x) ) is at -a and one at +a, if the energy is less than zero, there can be either one or two bound states, depending on the magnitude of α...if α is large enough, there can be two bound states, but if α is small, there...

I know coherent states are minimal uncertainty states and can provide a link from quantum to classical physics.But when I hear fermions can't have coherent states,or at least are limited in this sense,I can't see any relationship! What's the point? And...another thing...is there sth called...

Consider the Gaussian Integral (eqn 2.64).. is anyone able to explain how the constant of normalization is rationalised?

Homework Statement Explain why, as the atomic number increases, the 4s electronic states fill before the 3d states. The fact that they fill first means they are lower energy. You must explain why they are lower energy. Homework Equations The Attempt at a Solution First, I'm aware...

With great interest I read an article about a paper where scientists were able to create two photon bound states ("molecules of light"). http://physicsworld.com/cws/article/news/2013/sep/26/physicists-create-molecules-of-light I was quite astonished since light normally does not...

Homework Statement A particle of mass m is trapped in a one-dimensional infinite square well running from x= -L/2 to L/2. The particle is in a linear combination of its ground state and first excited state such that its expectation value of momentum takes on its largest possible value at...

Homework Statement In class, we discussed metal quantum dots, and we argued that they’re not so useful for device applications since the separation between energy levels for energies near the Fermi energy is much less than a typical optical photon energy of 2 eV. Let’s consider that...

My book gives a treatment of this problem for crystal vibrations, but I don't really understand it. It says: There is one allowed value of K per volume (2\pi/L)3. But at the same time it has just shown that Kx,Ky,Kz can take values ±2\pi/L which would certainly lead to more combinations of...

A particle of mass m is trapped in a one-dimensional infinite square well running from x= -L/2 to L/2. The particle is in a linear combination of its ground state and first excited state such that its expectation value of momentum takes on its largest possible value at t=0.I know the process of...

So, I've read conference proceedings and they appear to talk about counter-intuitive it was to create an infinite-energy state for the harmonic oscillator with a normalizable wave function (i.e. a linear combination of eigenstates). How exactly could those even exist in the first place?

Hi folks, I just have a question concerning whether it is possible to produce an ensemble of individual electrons in pure single-particle spin states. I'm assuming it is possible, but sometimes one hears that strictly speaking all electrons are entangled with one another, which would mean...

If problem states "acceleration is constant" what is the acceleration? While gliding down a steep hill, a bike rider experiences constant acceleration. After 4.50 seconds, he reaches a final velocity of 7.50 m/sec. The bike's displacement was 19.0 meters. I know that I'm supposed to be using...

Hi folks, I was just reading about symmetries, and why we say that the two spin states of the electron are states of the same particle, while we are free to say that the two strong isospin states define tow different types of particle. According to the book I'm reading, we must attribute two...

Homework Statement An electron in an infinitely deep potential well of thickness 4 angstroms is placed in a linear superposition of the first and third states. What is the frequency of oscillation of the electron probability density?Homework Equations E=hωThe Attempt at a Solution My main...

Hi, If you have a even-even nuclei which is deformed, you get a rotational spectrum of 0+,2+,4+,... I don't understand why the parities are positive for even I and why all members of a rotational band must have the same parity. I read about this in Krane's book: an introduction to nuclear...

Hi I read this information about the Qubit: "N Qubits are equivalent 2^N classical bits (2^N states)" But I couldn't understand that, because I know that each single Qubit could be one and zero at the same time, so each single Qubit is equivalent two classical bits (two states) That...

Hey guys, I was reading about thermal states and now I have a doubt: is a thermal state always a mixed state with density matrix ρ=exp(-βH)/Tr(exp(-βH)), or is there also a pure thermal state? Thank you

I'm having trouble finding comprehensible explanations of how experimenters can ever know that two particles are entangled. I understand that the first experimental confirmation of entanglement used Calcium or Mercury vapor which when excited gave off pairs of entangled photons. But how did...

Homework Statement 2) For an intrinsic (undoped) semiconductor at room temperature with the Fermi energy in the center of the 1 eV band gap, find the fraction of unoccupied electron states at the top of the valence band and the fraction of occupied states at the bottom of the conduction...

Homework Statement I need some help with the following problem: Homework Equations ##\rho(k) dk = \frac{L}{\pi} dk## ##L=Na## ##\omega^2= \omega_m^2 \ sin^2 (qa/2)## The Attempt at a Solution The density of states is given by: ##g(\omega)= \rho (k) / \frac{dw}{dk}## Where...

For an electron gas generated in the inversion layer of a semiconductor interface, my book gives the conduction band density of states for the two dimensional electron gas as: ##g(E)=\frac{L^2m^*}{\hbar^2 \pi}## Where m* is the effective mass of the electron. I can't follow how this was...

According to Griffiths QM book, after he derived the stationary state solutions to the Schrodinger equation for a particle in an infinite potential well, which are just functions of sine, he claims that these stationary solutions are orthogonal and complete. I agree that they are orthogonal...

hi i know what is coherent state, but i read this text in an article and i don't understand this " if we wish to describe long range macroscopic forces, only bosonic fields will do, since fermionic fields cannot build up classical coherent states. " can you explain it for me, how...

Ok, so for some reason this section of the GRE book makes 0 sense to me ... maybe because i haven't taken the class yet, maybe I'm missing something ... It says "If you have a spin-1 particle with m = +1 and a spin-1/2 particle with m = +1/2, then m_tot = +3/2 (this part makes sense, you just...

Hi folks --- I was just reading that entangled states are very much the norm in the universe. Can anybody tell me why entanglement is taken to be such a pervasive feature of the world, so that product states are the exception? Has it got something to do with the fact that strictly speaking all...

I look at wikipedia.org/wiki/Bell_state and use the same notations. The article says that there are just 4 Bell states. Is not |\xi^+\rangle = \frac{1}{\sqrt{2}} (|0\rangle_A \otimes |+\rangle_B + |1\rangle_A \otimes |-\rangle_B) another maximally entangled state? The Schmidt decomposition...

It just occurred to me that I don't know why composites of interacting particles are always in entangled -- as opposed to mere product -- states. Obviously if they are not interacting we will just represent them as being in a product state; but why is it that being in a product state entails...

In the use of the word "causation" can one say that one quantum state "causes" another if the two states are not measured? Or does the concept of causation only refer to a relationship between measurements?

I know how to calculate transition rates between nl resolved states in a hydrogen-like atom, but I don't know how to calculate transition rates between nljm states. I know that dipole transition rate is \frac{32}{3}\frac{\pi^3 \alpha c}{\lambda^3}\left<\psi_1|\mathbf{d}|\psi_2\right> The...

The result of the Kallen-Lehmann spectral representation is that the two point correlation (and thus also the full propagator) has a pole in the physical mass of the particle. In Peskin and Schroeder it is also argued that multiparticle states show up as a cut, but bound states can also show up...