State Definition and 1000 Threads

A question I have faced in exam to calculate ground state energy Given Hamiltonian 1/2m(px2+py2)+1/4mw2(5x^2+5y^2+6xy) ground state energy has to be obtained Its clear that the Hamiltonian is a 2D LHO Hamiltonian but what for the term 3/4(x+y)2

1. Problem Statement Find the steady state output yss(t) for the input u(t)=t-π in terms of an infinite sum of sinusoids. We are given the transfer function as: 2. Homework Equations G(i) = ... |G(ik)| = ... Φ(ik) = ... (this is the angle) yss(t) = βk||G(ik)|ei(kt+Φ(ik)) ***check that this...

Hello, Suppose that the angular momentum of a system can take the values 0, 1, 2. One carries out a measurement of ##J_z## on this system. What can be said about the state of the system after the measurement? To what extent can it be perfectly certain if ##J_y## and ##J_x## do not commutate...

Homework Statement I am trying to understand what the difference in the two questions (linked) are. I understand how to find the steady state response for x. Is the second question just asking for the first and fourth element in the Xss matrix? Homework Equations Xss=[q1 q2 q1dot q2dot] The...

I am trying to read through this paper discussing what quantum fluctuations mean in their various contexts, particularly in de Sitter space. I have come across this passage and am curious to what it actually means? https://arxiv.org/pdf/1405.0298.pdf pg. 10, second paragraph: "If a quantum...

Homework Statement The coefficient of thermal expansion and isothermal compressibility of a gas are given by ##\alpha_P =\frac{V-b}{TV}## and ##\kappa_T = \frac{V-b}{PV}## find: a) The equation of state b) If the heat capacity at constant volume ##C_V## is constant, what is ##\delta U##? c)...

What methods other than Light Dependent Resistor incorporation are there to determine the 'bulb state'? I'm guessing it's going to include the use of another type of optoelectric component? Thanks

Homework Statement A hydrogen atom is in the 7f state. What is the magnitude of its orbital angular momentum? Homework Equations L=sqrt(L(L+1)hbar The Attempt at a Solution L= Sqrt(3(3+1)Hbar) 1.41hbar (we want J*S) 1.41*1.054*10^-34 1.47*10^-34J*S

1. The problem statement Consider a particle of mass m under the action of the one-dimensional harmonic oscillator potential. The Hamiltonian is given by H = \frac{p^2}{2m} + \frac{m \omega ^2 x^2}{2} Knowing that the ground state of the particle at a certain instant is described by the wave...

I have a question about probability amplitudes to go from one state to another. I think it'll be clearest if I start with the case that I understand. Suppose I start in some initial state |ψ>, and I let it evolve over time t to some state eiHt/ħ|ψ>. Now, if I want to know the probability that...

Hi everyone, I was wondering if mu thinking was correct abut this argument, here is what I was thinking abut. A wave-function that is an eigenfunction of the Hamiltonian always describes a state of definite energy. Ok now let's say the eigenvalue is discrete so the wave-function belongs to...

I'm finishing my degree in Engineering Physics (really just physics). Without a doubt my favorite area of physics is solid state physics. While I love computational and theoretical work, I don't think making a career out of it is as easy as it is in the experimental or engineering side of it. So...

This is from *Statistical Physics An Introductory Course* by *Daniel J.Amit* The text is calculating the energy of internal motions of a diatomic molecule. The internal energies of a diatomic molecule, i.e. the vibrational energy and the rotational energy is given by...

Homework Statement State from the wavefunction: Ψ(x) = ∫(dk/2π) f(k) uk(x) Calculate the normalization <Ψ|Ψ> Homework Equations <Ψ|Ψ> = ∫|Ψ(x)|^2 dx The Attempt at a Solution [/B] Well I know the relevant equations, but I am not sure how to compute the integral in order to start...

Given that the Hamiltonian is H = P^2/(2m) + aδ(X − x(naught)) + bδ(X + x(naught), where x(naught) is a positive number. Find the conditions for bound states to exist and calculate their energies. Find the scattering matrix for arbitrary values of a and b. Can someone help me solve this please.

Dear all, I am using molecular dynamics to calculate energy for ionic liquid. In the article that is proposed equation of state that I want to use, the author would call the energy in the following formula(u) conformational(potential energy): (du/dv)T + T(dp/dT)V = ptot Firt T and V are...

The Hong-Ou-Mandel experiment is one of many examples where the amplitudes associated with two histories cancel out, leaving us with a reduced range of possible outcomes. Obviously, the total probability of those outcomes has to be unity. My question relates to the fact that these processes are...

Dear all, I want to calculate thermodynamical properties of my molecule which I am calculating its thermodynamical properties of non-ideal part using Molecular dynamics. I need ideal gas state total energy, Cp, and Cv in several different temperatures. I am using opt+freq at B3lyp/6-311++G(d,p)...

Homework Statement A p-state clock model is a spin model in which states can be viewed as hands of a clock! Now knowing the models we should prove these two models are equivalent for ##p=q=2## or ##p=q=3## Homework Equations Potts model is described by $$ H = -J \sum_{<ij> } \delta_{...

It's known that the time-translation operator is ##\exp(-i Ht)## and the space-translation operator is ##\exp(i (p \cdot x))##. The former causes a time-translation for a state vector whereas the latter causes a space-translation. Can we operate with the two operators on the state vector? Like...

The helicity in non relativistic quantum mechanics is given by ##\sigma \cdot p / |p|## where ##\sigma## are the pauli matrices and ##p## the momentum. In spinor space, the ##\sigma## are 2x2 matrices, and thus, the helicity, if we calculate it, is a 2x2 quantity. But in 3d physical space, the...

Homework Statement Part e) Homework Equations I know that the time evolution of a system is governed by a complex exponential of the hamiltonian: |psi(t)> = Exp(-iHt) |psi(0)> I know that |psi(0)> = (0, -2/Δ) The Attempt at a Solution I'm stuck on part e. I was told by my professor...

I have never heard a challenge by quantum entanglement to the concept that a state is a "property" of a particle, which I don't understand. I cannot see any way someone can interpret a state as a property of a system, rather than as a means of treating information about the system, given how...

Homework Statement Homework EquationsThe Attempt at a Solution This is the Solution. I am having trouble understanding parts of it. The first part I don't get is why the e^i... goes with the -z. Did my professor just choose one at random, or is there a specific reason? The second part...

The picture shows an experimental setup where one or more silver atoms are sent from an oven through 3 Stern-Gerlag (SG) filters with outputs from E and F going to detectors. If C and D remain coherent they can recombine to restore the original state and the particles all go through port E. If...

Hello, I got this problem but I don't know How can Find Heat loss (or gain) - Q3 - from the curved surface of the metal rod to the surrounding. This is the problem: A metal rod, of diameter (d) and length (L), runs between two hot walls at temperatures, T1 (Wall 1) and T2 (Wall 2)...

Homework Statement Homework Equations I know that there are two eigenstates of the operator C: |B> = (1 0) as a column vector with eigenvalue 1 |R> = (0 1) also a column vector with eigenvalue -1 The Attempt at a Solution I'm attempting to solve part c (second image). My initial...

Homework Statement Homework Equations I know that there are two eigenstates of the operator C: |B> = (1 0) as a column vector with eigenvalue 1 |R> = (0 1) also a column vector with eigenvalue -1 The Attempt at a Solution My work is shown here: If anyone could point me in the right...

Hello, I have studied about heat transfer through conduction only in steady state but I wondered about this problem that I created. Suppose you have a box that is insulated from all sides but Suppose a constant heat flow from that wall. Inside that box you have M kg of water at the same...

In driven SHM, we ignore an entire section of the solution to the differential equation claiming that it disappears once the system reaches a steady state. Can someone elaborate on this?

Homework Statement Homework Equations $$\frac{\partial S}{\partial u}\Bigr|_{v} = \frac{1}{T}$$ $$\frac{\partial S}{\partial v}\Bigr|_{u} = \frac{-P}{T}$$[/B] The Attempt at a Solution a.) $$\frac{S}{R} = \frac{UV}{N} - \frac{N^3}{UV}$$ $$\frac{S}{R} = \frac{UV}{N} - \frac{N}{uv}$$ $$...

Hi. 1. Does a pure state belong to mixed states \hat{\rho}=\sum_k p_k|\psi_k><\psi_k| where ##p_k=1## for k=i and otherwise 0 ? 2. Does quantum jump by observation work for both mixed and pure states ? Your teachings will be appreciated.

Suppose I want to find the ground states corresponding to several Hamiltonian operators ##\left\{ \hat{H}_i \right\}##, which are similar to each other. As an example, let's take the ##\hat{H}_i##:s to be anharmonic oscillator Hamiltonians, written in nondimensional form (##\hbar = m = 1##) as...

I am trying to understand what space is. Does QM state that Space is made of nothing? In other words it does not exist?

Hello guys, I am trying to understand the following experiment: 1. Prepare a 2 level atom in state |0> 2. Shine in a Pi/2 pulse --> atom goes to 1/√2 (|0>+|1>) 3. Wait time T 4. Shine in second Pi/2 pulse a) if the state is pure: atom will go to state |1>, p1=1 b) if the state is...

In paper PRL 101, 246807 (2008), authors use "Peierls substitution", that is ky -> -i∂ y. As we know, ky is eigenvalue of translation operator in period potential, while -i∂ y is momentum operator, it seems they are huge different. So I wonder how to get ""Peierls substitution" in strict math way?

Homework Statement The constant-volume heat capacity of a particular simple system is c_v = AT^3 where A is a constant. In addition the equation of state is known to be of the form (v-v_0)p = B(T) where B(T) is an unspecified function of T. Evaluate the permissible functional form of B(T)...

I've seen some popular news articles discussing cellular regeneration research carried out at the Wexner medical center in Ohio State University by Chandan K Sen and others . I was wondering if anyone had a source for more information (and more reliable than the popular press) on the topic...

Yah electrons existing the lowest possible energy state! Now suppose, we throw a beam of light towards a ground state of a atom. I heard/know electrons will take up energy from the photon "hv", and go to the next energy level i.e. excited state. Now my point is, is it only the valance electron...

Hi, I want to simulate a forced convection cooling problem. Air at ambient temperature is forced through a fan into a system to cool electronics and I would like to assess the temperature of the outlet air. Actually I'm interested in the delta between the ambient and outlet temperature. This...

Hi! So I just breezed through a summer Calc II course (took E&M and Modern Physics last semester) and will be approaching Solid State Physics and Calc III this coming semester together. I've taken my school's upper division Linear Algebra course and passed before last semester and continue to do...

I've read that if a given spacetime possesses a timelike Killing vector, then it is possible to define a unique vacuum state by constructing positive and negative frequency modes with respect to this timelike Killing vector. My question is, what does this mean? Explicitly, how does one use a...

If we switch a super-conductor between normal and Meissner states, using varying magnetic field, there has to be some delay from when the field exceeds the critical field to the appearance of Meissner state. Have there been any experimental measurements of this delay? What are the measured values?

Actually those to subjects are in our syllabus now! Please suggest me some books which will be easy to understand and somewhere maintain my academic syllabus too !

A mixed state is when the system is actually in one state or another, but you just don't know which, and you use probabilities to describe your uncertainty. I'm referring to a mixed state of the entire system. I want an actual example. Can you think of some? Note I wasn't describing mixed state...

I know that Quark-gluon plasma is the hotter state of matter that we know. Soo is solid the coldest state of matter ? If there is no so sorry for my stupid brain!

I would like to know what the "0-ket", called vacuum state and used in the following expression, represents $$\Psi(x,t) = \int d^3x <x| \ a^{\dagger}(x) \ |0>$$ I have rewritten the expression for the case of just one ##x##. The expression above is usually presented with ##(x_1,...x_n)## (n...

Homework Statement This is a state ecuation of a gas: PV=AT+B/V, where A and B there are constants. First: Demonstrate that ##c_V## depends only of T Second: Find U(T,V) and S(T,V) Homework Equations ##\left(\frac{\partial U}{\partial S}\right)_V=T\text{ (1)}## ##\left(\frac{\partial...

I have the following non-stationary state of the QSHO: Ψ = [ e −3iωt/2 + []e −5iωt/2] where β = mω/ħ in calculating <E2> The answer I see in the textbook is 6.17 ħ2ω2. This answer suggests that in calculating <E2> = ∫ Ψ*Ĥ2Ψ dx where Ψ is composed of the above two terms Ψ1 and Ψ2 (a linear...

On what does the stiffnes/softness of the SN EOS depends? How does it change with temperature, progenitor mass, or other parameters like compresibility, symmetry energy etc? Would softening in NS EOS lead to softening in SN EOS? Tnx, Cheers