Time dependent Definition and 120 Threads

Hello! I am reading this paper and in deriving equations 6/7 and 11/12 they claim to use second oder time dependent perturbation theory (TDPT) in order to get the correction to the energy levels. Can someone point me towards some reading about that? In the QM textbooks I used, for TDPT they just...

THe question is pretty simple. I was doing an exercise, in which $$p = \lambda P, Q = \lambda q$$ is a canonical transformation. We can check it by $$\{Q,P \} = 1$$ But, if we add $$t' = \lambda ^2 t$$, the question says that the transformation is not canonical anymore. I am a little...

The transition probability -- the probability that a particle which started out in the state ##\psi_a## will be found, at time ##t##, in the state ##\psi_b## -- is $$P_{a \to b} = \frac{|V_{ab}|}{\hbar^2} \frac{sin^2[(\omega_0 - \omega)t/2]}{(\omega_0 - \omega^2}.$$ (Griffiths, Introduction...

Given a wavefunction ψ(x, 0) of a free particle at initial time t=0, I need to write the general expression of the function at time t. I used a Fourier transform of ψ(x, t) in terms of ψ(p, t), but, i don't understand how to use green's functions and the time dependent schrodinger equation to...

If I plug the solution into the Schrodinger equation I get $$(i \hbar \partial_t - H)\ket{\psi} = 0$$ Since I know that the zeroth-order expansion is lambda is already a solution I think this is equal to $$(i \hbar \partial_t - H)e^{i\phi} e^{-i\gamma}\ket{\delta n} = 0$$ If now I carry on with...

What I have tried is a completing square in the Hamiltonian so that $$\hat{H} = \frac{\hat{p}^2}{2} + \frac{(\hat{q}+\alpha(t))^2}{2} - \frac{(\alpha(t))^2}{2}$$ I treat ##t## is just a parameter and then I can construct the eigenfunctions and the energy eigenvalues by just referring to a...

U=-∫F*v*dt= -∫(m*g/3)*cos(ω*t) dt = -(m*g/3 )* (v/ω )* sin(ω*t) except that according to the official solution, I should be getting positive sign instead of negative. Am I doing something wrong?

I am assuming this is the interaction picture, so I start with $$|\psi>=c_1(t)|1>+c_2(t)|2>$$. Plugging this into the Schrodinger equation, I get the equations $$i\hbar c_1(t)=<1|H'|2>c_2(t)$$ and $$i\hbar c_2(t)=<1|H'|2>c_1(t)$$. I am assuming H' (the perturbation) is $$H'= − f(t)[...

An electric field E(t) (such that E(t) → 0 fast enough as t → −∞) is incident on a charged (q) harmonic oscillator (ω) in the x direction, which gives rise to an added ”potential energy” V (x, t) = −qxE(t). This whole problem is one-dimensional. (a) Using first-order time dependent perturbation...

Is time dependent on the motion of everything in the universe? If all motion was played in reverse, so particles gain kinetic energy from sound and heat energy as they move the opposite direction, and light retreats into the sun, would time technically now be flowing backwards? If all matter (so...

If a Lagrangian has explicit time dependence due to the potential changing, or thrust being applied to the object in question, how does calculus of variations handle this? It's easy to get the Lagrange equations from: δL = ∂L/∂x δx + ∂L/∂ẋ δẋ What is not clear is how this works when t is an...

Homework Statement Suppose the potential in a problem of one degree of freedom is linearly dependent upon time such that $$H = \frac{p^2}{2m} - mAtx $$ where A is a constant. Solve the dynamical problem by means of Hamilton's principal function under the initial conditions t = 0, x = 0, ##p =...

Hello, I'm lost at where to go after drawing bifurcation diagram of $$\dot{x} = r + x - x^3.$$ If we also assume our parameter is time dependent such that $$\dot{r} = -\delta x.$$ How could we use our initial bifurcation diagram to sketch solutions for small δ?

Homework Statement A positron is moving in a circular orbit of radius r = 2cm within a uniform magnetic field B0 = 50##\mu##T. The magnetic field varies over time according to the expression: B = 700t + Bo and, therefore, each orbit can be considered almost circular. (a) Calculate the...

Homework Statement Calculate the time-dependent magnetic field intensity B(t) at an axial distance r from a long, thin straight copper wire that carries a sinusoidal current with an alternating frequency of 50 Hz and a maximum amplitude of 0.5 A. Homework Equations I = Asin(\omega t) B =...

Homework Statement [/B] Calculate the rate of ionization of a hydrogen atom in the 2p state in a monochromatic external electric field, averaged over the component of angular momentum in the direction of the field. Ignore the spin of the particles. In this case we can write...

Homework Statement A proton is initially located at the origin of some coordinate system (at rest), when a time-dependent force, $$F(t)=F_0\sin{(\omega t)},$$ is applied to it, where ##F_0## and ##\omega## are constants. a) Find the velocity and displacement of the proton as functions of...

Homework Statement The answer is as follows: [/B] However they said that time t=0 so I am confused how the exponent has a t in it surely it should be zero. Thanks

Homework Statement [/B] Here's the problem from the homework. I've called the initial positions in order as 0, l, and 2l. Homework Equations The most important equation here would have to be |V - w2*M| = 0, where V is the matrix detailing the potential of the system and M as the "masses" of...

Homework Statement Homework EquationsThe Attempt at a Solution I tried to solve (a), but i don't know which approach is right ((1) or (2)) and how to solve (b).[/B]

Hi all, I have a doubt that I would like to solve with oyu help. Basically I want to calculate forces on a solenoid due to the magnetic field it produces and than calculate deformation. I consider 2 cases: 1/ Static I did analytic calculation for force calculation, and i made FEM simulation...

The problem looks very simple. We have a time-dependent Hamiltonian: $$H(t) = B(t)H_0$$, where ##B(t)## is a numerical function, and matrix ##H_0## is time-indpendent. Let us consider: $$B(t) = \begin{cases} 1,&\text{for $0\leq t\leq t_0$}\\ A,&\text{for $t>t_0$.} \end{cases}$$ Also, let us...

Homework Statement Random given wavefunction,say $$\Psi (x) = N e^{- \mu x}$$ in a V(x) e.g. infinite well .Find ## \Psi (x,t) ##. Homework Equations - The Attempt at a Solution If the wavefunction is given as the sum of eigenfunctions,you just multiply them by ## e^{-i...

Homework Statement Solve the time dependent 1D heat equation using the Crank-Nicolson method. The conditions are a interval of length L=1, initial distribution of temperature is u(x,0) = 2-1.5x+sin(pi*x) and the temperature in the ends of the interval are u(0,t) = 2; u(1,t) = 0.5. Homework...

I have a question about time dependent perturbation. In time dependent perturbation, unlike time independent perturbation, there is no lamda which is used for comparing order. So, I`m confused how can I determine order. Is there any explanation which use lambda or some other method for...

Consider a particle moving near the ground with the ground surface as the zero-point potential reference. If at time t we apply an electric field, say parallel to gravity force, where we should consider as a zero-potential reference point? Does the energy remain conserved (Is the energy equal to...

Hi. I have been looking at some notes for time dependent perturbation theory. The equation for the transition probability involves the matrix element < f | H | i > where f is the final state , i is the initial state and H is the perturbation switched on at t=0. If H is a constant , ie. just a...

In field theory we most of deal with theories whose Lagrangian densities are of the form (sticking to scalar fields for simplicity) $$\mathcal{L}= -\frac{1}{2}\partial_{\mu}\phi\partial^{\mu}\phi - \frac{1}{2}m_{\phi}^{2}\phi^{2} + \cdots$$ where ##\partial := \frac{\partial}{\partial x^{\mu}}##...

How would I calculate the rate that water would boil off? I've done a lot of looking into and found an equation but it doesn't seem quite right. What I found states that the KJ/h delivered to the water divided by the latent heat energy gives you the amount of water that will boil off. I tried...

Hello forum, The kinematic equations for motion with constant acceleration are: v_f = v_0 + a*t x_f = x_0 + v_0 * t +(0.5) a*t^2 The acceleration a is a constant. Is it possible to use them if the acceleration is not constant but a function of time? For example, a(t)= 3t^2+2? Can we simply...

Homework Statement Hi! I really need help with finding time- dependent continuity equation for electron densities in the atmosphere. I've tried to solve it without any success. My question is if someone can give me a good link/link or equations that I can start with. Homework Equations See...

Hello, I have a simple question. Suppose a perfect point source in front of a mirror. The virtual image of the point source acts like a second point source. Now let's look at the interference of the direct point source light and the virtual point source, at some position. Since the path...

Homework Statement Let |v(t)> ∈ℂ^2 by the time-evolving state of a qubit. If |v(0)> =\begin{pmatrix} 0 \\ 1 \end{pmatrix} , and the Hamiltonian of the system is H = \begin{pmatrix} 0 & -iλ \\ iλ & 0 \end{pmatrix} (where λ∈ℝ) what is |v(t)>?Homework Equations Time dependent schrodinger...

Ok so for equations of spherical wave in fluid the point source is modeled as a body force term which is given by time dependent 3 dimensional dirac delta function f=f(t)δ(x-y) x and y are vectors. so we reach an equation with ∫f(t)δ(x-y)dV(x) over the volume V. In the textbook it then says that...

I have two signals (time series) shown in the plot below. Just by looking at the figure, we can see that the two main peaks of both signals are very closely aligned (correlated), however the red signal has additional features elsewhere which don't match the blue curve. I am looking for some...

1. Homework Statement p: momentum x: position t: time h_bar: Planck's constant Ψ: wave function Homework Equations The Attempt at a Solution I've posted a link to pictures. http://imgur.com/a/TKvUu I'm not vera good at using LaTex yet :( So I've shown that the wave equation satisfied the...

Homework Statement A particle of mass m is subject to a force F(x) = −kx^−2 (1) that attracts it toward the origin. (a) Determine the potential energy function U(x), defined by F(x) = − d U(x)/dx. (b) Assuming that the particle is released from rest at a position x0, show that the time t...

I was wondering... can the rest mass of an object be time dependent? Like in a scenario where the body is losing mass? (Sorry I meant for a title "rest mass time dependent?")

Hi All, I have problem in understanding one step in the derivation of the time dependent Schrodinger Equation. Please see attached file page 2 (marked in red). Most grateful if someone can help! Peter Yu (This is from Quantum Mechanics The Theoretical Minimum Page 99-102)

Define energy as E=T+U. For anyone using different terminology, by rheonomic (time dependent constraints) I mean that if a system has N degrees of freedom, the position vectors of each particle of the system are given by ##\vec{r}_i(q_1,q_2,...,q_n,t)##. Where ##q_i## are generalized...

Homework Statement A particle of mass m is confined to a space 0<x<a in one dimension by infinitely high walls at x=0 and x=a. At t=0, the particle is initially in the left half of the well with a wavefunction given by, $$\Psi(x,0)=\sqrt{\dfrac{2}{a}}$$ for 0<x<a/2 and, $$\Psi(x,0)=0$$ for a/2...

Homework Statement A quantum particle of mass ##m## is bound in the ground state of the one-dimensional parabolic potential well ##\frac{K_0x^2}{2}## until time ##t=0##. Between time moments of ##t=0## and ##t=T## the stiffness of the spring is ramped-up as ##K(t) = K_0...

If you are given the state of a system at t=0 in vector form, how do you find the wave function for arbitrary t?

when do you call a spacetime dynamical...when metric is time dependent or it depends on space ??...

Homework Statement I have a problem with the next situation. I have a magnetic dipole moving at constant speed on the z axis. On the plane z=0 I have a circular wire with a resistance R and radius a. I have to calculate the electromotive force on the wire as a function of the speed of the...

I am looking for a realistic explanation of the double-slit experiment in terms of wave packets (instead of stationary waves). First of all this results in using the scattering cross section, i.e. the probability current (not the density). Then, I guess, there is a kind of time average. So one...

Let: $$x_1=A\sin{\omega t}$$ $$x_2=\dot{x}_1=A\omega \cos{\omega t}$$ $$y=A\omega$$ We want to represent this system in a state space model. The state transition matrix read: $$A=\begin{bmatrix} 0 & 1 &\\ -\omega^2 & 0 \\ \end{bmatrix}$$ I am not sure what the output matrix will be like. Can we...

I am would like to solve this differential equation: Where http://ieeexplore.ieee.org.ezproxy.uniandes.edu.co:8080/ielx5/8/6493417/6409989/html/img/6409989-eqdisp-3-small.png Could you give me some practical ideas about the required software and methodology? Thank you very much

The wave function solution psi is a function of time and position. Hence the integral of its square over all x will, in general, give a function of time. To normalize this, we must multiply with the inverse of the function. Therefore it seems that the normalization constant does not remain...

Homework Statement If A is a time dependent vector, calculate [itex] \int_{t1}^{t2} dtA(t) \times \frac{d^2A}{dt^2} [\itex] Homework Equations The Attempt at a Solution I think we should somehow relate it with something's derivative. \int_{t1}^{t2}A(t)\frac{d^2A(t)}{dt^2}dt=...