Time dependent Definition and 130 Threads

Homework Statement Let H= \frac{1}{2}m(V_x^2+V_y^2+V_z^2)+u(\vec{Q}) be the hamiltonian operator for a particle which has mass m>0 with u(\vec{Q})=\lambda_0 (Q_x^2+ Q_y^2). Knowing that [Q_\alpha, m V_\beta]=i \delta_{\alpha \beta}. Show that If \displaystyle A_\alpha= \frac{d...

Klein–Gordon equation with time dependent boundary conditions. Suppose we look for solutions to the Klein–Gordon equation with the following time dependent boundary conditions, psi(r,theta,phi,t) = 0 zero at infinity psi(on surface of small ball, B_1,t) = C*exp[i*omega*t] psi(on...

Hi I was wondering if someone could help me out. I have been studying TDPT and was wondering how it applies to atomic physics or if someone could give me a example that would be great.

I'm having trouble understanding why a derivative of a time dependent vector function is orthogonal to the original function. Can anybody give me some enlightenment? I searched around for some previous talk about this, and I can't find anything. Thanks.

Have been struggling with errors galore on this one. I am not too conversant with ODEs in MATLAB. The problem is as follows. I have to solve these two ODEs for A1 and A2. A1dot = k2*A2 - k1*A1 - k3*A1/(k4 + A1) + R A2dot = k1*A1 - k2*A2 Here R is a function of time defined as follows...

Does anyone kown how to apply time dependent perturbation theory to densities matricies (I'm interested in first order)? Thanks.

This isn't a homework question per se, but it is from a (graduate) textbook. I'm not taking a course in this, but I've been trying to learn some basic chemical kinetics and couldn't find other problems like this one. Homework Statement The rate of the reaction CH5NH2(g) -> C2 H4(g) +...

Can someone explain the components of the Time dependent Schrodinger equation for me. Thank you -H

Let's say that L=((1/2)m*v^2-V(x))*f(t), or something similar. What are the equations of motion? For time independent it should be: (d/dt) (dL/dx_dot)=dL/dx . Using this I get m\ddot{x}+m f_dot/f x_dot+dV/dx=0. Is this right? I keep thinking about the derivation of the equations and it...

A friend of mine lead me to this math example when I asked him what math would be involved in finding the deceleration necessary to stop an already accelerated object over a certain distance. For example, a car going 50mph that must stop in 40ft. This was the example... ...and I have no idea...

Homework Statement A system with only one degree of freedom is described by the following Hamiltonian: H = \frac{p^2}{2A} + Bqpe^{-\alpha t} + \frac{AB}{2}q^2 e^{-\alpha t}(\alpha + Be^{-\alpha t}) + \frac{kq^2}{2} with A, B, alpha and k constants. a) Find a Lagrangian...

I am to design a gearbox for a small spring powered dragster. It needs to complete a track of 10 m, so I want the spring to give out it's energy over this distance, but without causing wheel slipping. I also need to produce graphs: acceleration vs time, velocity vs time and distance vs time...

Hi, In the free theory \mid k \rangle=a^{\dag} (\vec{k}) \mid 0 \rangle . Then in Srednicki chapt 5, he defines time-independent operator that he says in free theory creates a particle localized in momentum space about \vec{k_1} as: a^{\dag}_1 \equiv \int f_1 (\vec{k}) a^{\dag}(\vec{k})...

(Sorry for my poor English, Please, forgive mistakes, if any.) Dear Friends Not doubts about what is to be meant for "conservative vector field" as far as time independent fields are concerned. But what about non stationary fields? I thought it was a meaningless concept when field is...

Hi there any body know that mcnpx has abality to do time dependent calculations? please lead me quickly, I need it. regards

Homework Statement The Force is F(x)=Av2/x. find x(t) if x(0)=0 and vx(0)=0 Homework Equations The Attempt at a Solution My issue is that i set this up as mdv/dt=F but when i try to separate the variables i don't know what to do about the v since it depends on x. any suggestions?

Homework Statement Show that Y(x,t) = cos(kx)exp(-iwt) is a solution to the time-dependent Schrodinger wave equation. where k is the wavenumber and w is the angular frequency Homework Equations Hamiltonian of Y(x,t) = ihbar d/dt Y(x,t) The Attempt at a Solution When I plug...

Hi all, I am struggling to solve some simple state equations in the following form. dx/dt = A x + bu solution is simple if A has only constant elements, because i can multiply both sides with exp(-At) and solve. in my case, A has time dependent elements. i know their functions. is...

Could someone guide me step by step from the free SE to T(t)=e^(iE_n t)/\hbar ? I am not really familiar with PDEs of any kind and I would like slow step by step analysis! I am just confused by the great many ways of getting from there to there I find in books and Internet, so I would like...

Homework Statement Question: If a particle is in the ground state at time t<0, use the 1st order time dependent perturbation theory to calculate the probability that the particle will still be in the ground state at time t. Suppose we turn on the perturbation at time t=0 H(x) = ax...

Homework Statement V= V0 (r) + V1(r,t) V0 (r) =-e^2/r V1(r,t) is a small perturbation which is being activated only in the interval 0<t<tf The system starts in the ground state, where l =0 1. If the change in the potential is very slow, what is the probability of finding the system at tf...

A solution to time dependent SE but not Time independent SE?? How is it possible that a wave function is a solution to the time dependent schroedinger equation, but not to the time independent schroedinger equation (without time factors tacked on) with the same potential? I had this case on my...

I need some help with time dependent equations. I have two electrically charged particles in space that are at large distances. How would I write a time dependent equation to simulate there positions at give times. I know there initial positions and there initial velocities. And for...

Homework Statement (the actual question is now as an attachment) Assuming that the perturbation V(x,t)=\betax exp(-\gamma t) is applied at t = 0 to a harmonic oscillator (HO) in the ground state, calculate to the first approximation the transition probabilty to any excited state n\geq1...

Given an operator \hat{Q} (in the Schrodinger picture) in non-relativistic quantum mechanics and a state |\psi(t)\rangle such that \hat{Q} |\psi(t)\rangle=q(t)|\psi(t)\rangle where q(t) is explicitly time-dependent, can we properly say that |\psi(t)\rangle is an eigenstate of Q with a...

Homework Statement The equation of motion of a free electron in an electric field is m((d^2)x)/(dt^2) = -eE (Eq. 1) If x and E have the time dependence exp(iwt), where w=angular frequency, then -(w^2)mx = -eE (Eq. 2)...

how would i do this... A particle moving along the x-axis has its position described by the function x=( 2.00 t^{3}- 5.00 t+ 1.00 )\; {\rm m}, where t is in s. At t= 4.00 , what are the particle's position- i calculated that to be 109m , velocity, and acceleration? i have tried for over an...

In chapter nine of Griffiths' Quatum Mechanics text, he talks about the method of succesive approximations as a method for solving a two level system in time dependent perturbation theory. d(ca)/dt = f(t) cb --> ca_n = int[ f(t') * cb_n-1, dt', 0 t] d(cb)/dt = g(t) ca --> cb_n = int[ g(t') *...

So, you have an uniform merry go round with solid disc radius R and mass M1. It is set spinning with initial angular velocity of omega naut. If it stops after time t1, find magnitude of constant frictional torque that slows it down. M1 = 243 kg, R = 2.3m, omega nau = 2.5 rad/s, t1 = 30.1 s...

Hey people, I just finished reading a chapter in a book on quantum mechanics that has deeply disturbed me. The chapter was about symmetry in quantum mechanics. It was divided in two basic parts: time dependent and time independent transformations. Time independent transformations were...