Time dependent Definition and 130 Threads

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=...

Homework Statement Show that the wave function ##\Psi(x,t)=Asin(kx-ωt)## does not satisfy the time dependent Schrodinger Equation. Homework Equations ##-\frac{\hbar}{2m}\frac{\partial^2\psi(x,t)}{{\partial}x^2}+V(x,t)\psi(x,t)=i\hbar\frac{\partial\psi(x,t)}{{\partial}t}## The...

For part a I have (H0-ω\hbarm)|nlm>, which I think the (H0-ω\hbarm) part is the eigenvalue of the Hamiltonian, also is the energies? And mainly, I am not sure how to approach part b, the time variable is not in any of the states. I saw this in our lecture notes: ψ(r,t)=∑Cnψn(r) e-iEnt/\hbar...

Homework Statement We want to get the time evolution of a wavefunction and the expectation value of the Hamiltonian, and from there we can show that it's the same as the time-independent result. So to be clear: given a wavefunction, get the time evolution of that function and the expectation...

Homework Statement A particle is in a bound state of the infinite square well. It is in a state represented by the following wavefunction, written here at t=0: ψ(x)= -√(2/3)√(2/L) * sin (3πx/L) + i*√(1/3)√(2/L) * sin (2πx/L) (a)Write the full time-dependent wavefunction for this state...

Homework Statement A particle of mass m moves in a circle of radius R at a constant speed v. Assume: The motion begins from the point Q, which has coordinates (R, 0). Determine the angular momentum of the particle about point P, which has coordinates (−R, 0) as a function of time. The...

Homework Statement A long, straight, copper wire has a circular cross section with radius R, resistivity p and permittivity ε. If the current through the wire at any time t is sin(ωt) amperes, find the magnitude of the magnetic field B at time t a distance r from the centre of the wire for r >...

Hello, I am looking for some time dependent exact solution of Einsteins eqs. If I am right (if not please correct me) the easiest one is Robertson - Walker cosmological solution for homogeneous and isotropic universe (this use Oppenheimer and Snyder for collapse). I can't find another in...

Homework Statement An infinite straight wire carries a current I that varies with time as shown above. It increases from 0 at t = 0 to a maximum value I1 = 5.2 A at t = t1 = 15 s, remains constant at this value until t = t2 when it decreases linearly to a value I4 = -5.2 A at t = t4 = 26 s...

Homework Statement Problem is attached Homework Equations A formula sheet is also attached The Attempt at a Solution flux=\intB dA from .31m to .82 B=u I(enclosed)/2(pi)(d) d=x dA=dx L so ∫ (u)(I)(L)dx / 2(pi)(x) from .31m to .82m remember x=d in the pic. My answer is 3.9687e-7 and its...

Homework Statement Two identical spin-1/2 particles interact with Hamiltonian H0=ω0 S1.S2 where ω0>0. A time dependent perturbation is applied, H'=ω1 (S1z-S2z) θ(t) Exp[-t/τ], where ω1>0 and ω1<<ω0. What are the probabilities that a system starting in the ground state will be excited into each...

i have the basic question of special relativity why time , length and mass is a function of velocity here? i may know the mathematical interpretation of special relativity but i did not understand it physically how time can depend on these parameters. some please make me clear on this issue regards

Homework Statement See attachment Homework Equations The Attempt at a Solution (i) |\Psi(t)_{1}>=e^{{-itE_{1}/\hbar}}\frac{1}{\sqrt{2}}(|z^{+}>+|z^{-}>) |\Psi(t)_{2}>=e^{{-itE_{2}/\hbar}}\frac{1}{\sqrt{2}}(|z^{+}>-|z^{-}>) where...

Consider the attached exercise. I am having some trouble understanding exactly what time dependent hamiltonian it refers to. Because from the equation it refers to it seems that the hamiltonian is by definition time independent. Am I to assume that the H diagonal is a time independent...

I understand that in general, it's not true that in the case of a time dependent hamiltonian, the exponential map of the Hamiltonian is not a unitary transformation/the time evolution operator? U(t) \ne e^{-i \frac{H(t)}{\hbar} t} Is this thing allegedly not unitary or is it just not time...

Homework Statement The current in amps through a resistor with a resistance of 90 Ohm varies according to I=2.8e^(−7.6t) when t is in seconds. What is the total energy dissipated in the resistor from 0.5 to 1.4 seconds, written in Joules? Homework Equations I(t)=dQ/dt dU=dQ*dV...

Hi there. I'm dealing with this problem, which says: At time ##t=0## a constant and uniform electric field ##\vec E## oriented in the ##\vec x## direction is applied over a charged particle with charge ##+q##. This same particle is under the influence of an harmonic potential...

Time dependent wave equation trouble! Homework Statement I'm having heaps of trouble getting my head around the time dependent wave function and the use of operators to find measurement/probabilities etc... I'm having trouble with something like the following, If have a 1D inf potential...

Homework Statement A particle of mass m in the one-dimensional harmonic oscillator is in a state for which a measurement of the energy yields the values hω/2 or 3hω/2, each with a probability of one-half. The average values of the momentum <p> at time t = 0 is √mωh/2. This information...

Hi i have the differential equation \frac{d^{2}}{dt^{2}}X(t) +(A+B\frac{sin^{2}(mt)}{mt})X(t) I have tried by hnd to solve this and am getting knowhere does anyone know how to solve it and then plot X against t (where the constants A, B and m will be arbitrarily added), possibly using maple? I...

Hi, I'm trying to find a toy (i.e. analytic) example of a nonlinear system that has very different behavior for two different types of forcing: 1) \frac{\partial u(x,t)}{\partial t}+ N(u(x,t)) = F(x) where u(x,t) is the dependent variable, N represents some nonlinear operator with only...

I'm trying to simulate wavepacket propagation in various potentials (so far in 1D). I'm writing in C++, and using allegro graphics library. The TDSE is: \frac{∂ψ}{∂t} = \frac{i \hbar}{2m} \frac{∂^2 ψ}{∂ x^2} - \frac{iV}{\hbar}ψ So what I've done was writing out the real and imaginary parts...

To cut to the chase, I have to solve for the evolution of a two-state system where the system's state at time t satisfies the equation \mathrm{i}\hbar\left( \begin{array}{cc} \dot{c}_1(t)\\ \dot{c}_2(t) \end{array} \right)=\left( \begin{array}{cc} 0 & \gamma...

I was wondering if anyone has any actual data on the surface temperature of a fuel rod as a function of time. I am really curious as I am trying out a model I found which uses the fractional calculus. Or if anyone could point in the right direction to find said data that would be great as well.

Hey, I'm struggling to understand a number of things to do with this derivation of the scattering amplitude using time dependent perturbation theory for spinless particles. We assume we have some perturbation 'V' such that : \left ( \frac{\partial^2 }{\partial t^2}-\triangledown ^2 +...

Homework Statement A 4.00-kg particle moves along the x axis. Its position varies with time according to x = t + 2.0t^3, where x is in meters and t is in seconds. Find (a) the kinetic energy of the particle at any time t, (b) the acceleration of the particle and the force acting on it at...

Okey, so I´m taking a course in QM and I feel that I got a grip of most of it. But then we arrive at this formulea i\hbar\frac{\partial}{\partial t} c_n(t) = \sum_m \hat{V}_{nm} e^{i\omega_{nm} t}c_m(t), where \omega_{nm} \equiv \frac{(E_n - E_m)}{\hbar}. In other words time dependent...

While I was studying Ch 2.5 of Sakurai, I have a question about Green's function in time dependent schrodinger equation. (Specifically, page 110~111 are relevant to my question) Eq (2.5.7) and Eq (2.5.12) of Sakurai say \psi(x'',t) = \int d^3x' K(x'',t;x',t_0)\psi(x',t_0) and...

Hello, I am trying to self learn a little bit of quantum mechanics in order to describe the magnetic resonance phenomenon. I am following Griffiths book and i am understanding most of it. Now, there is a particular thing that is bogging me. The Schrodinger equation can be easily...

Homework Statement I'm looking at the 1d harmonic oscillator \begin{equation} V(x)=\frac{1}{2}kx^2 \end{equation} with eigenstates n and the time dependent perturbation \begin{equation} H'(t)=qx^3\frac{(\tau^2}{t^2+\tau^2} \end{equation} For t=-∞ the oscillator is in the groundstate...

Homework Statement An infinite straight wire carries a current I that varies with time as shown above. It increases from 0 at t = 0 to a maximum value I1 = 2.1 A at t = t1 = 14 s, remains constant at this value until t = t2 when it decreases linearly to a value I4 = -2.1 A at t = t4 = 24 s...

Homework Statement Below is a wave function that is a linear combination of 2 stationary states of the infinite square well potential. Where ψ1(x) and ψ2(x) are the normalized solution of the time independent Schrodinger equation for n=1 and n=2 states. Show that the wave function is...

Homework Statement a single loop of wire with radius A is rotating in a uniform magnetic field at angular frequency ω. The loop of wire drives a current through a resistor R. Determine the torque as a function of time needed to turn the wire. Homework Equations 1) Emf = ∫Fmag.dl...

It doesn't seem like a time dependent hamiltonian would have stationary states, am I wrong? I've run into conflicting information.

What is the definition of energy for quantum systems with time dependent Hamiltonians? Is it the eigenvalue of the Hamiltonian? (The eigenvalue is, in general, time dependent). However, the eigenstates of the Hamiltonian (even if it is time dependent) are stationary states, and hence no...

How do I handle the following situation. I have two time series, A and B. For the entire 100 yrs, we have P(A|B) ≠P(A), and Chi squared test leads us to reject the hypothesis of independence. But, If I break the data down into 10 yr chucks, I find that for some 10 yr chucks P(A|B) = P(A)...

I read from a book that the "total energy is not preserved when the potential depends explicitly on time", i.e. U(x,t). Can anyone show or prove it? Many thanks.

Hi, may potential, time dependent force field be called conservative? If so, the mechanical energy conservation of an isolated mechanical system does not hold in such field? Thanks.

Homework Statement A mass m is suspended by a massless string of varying length l = l0 - vt, where v is constant. The mass is released at angle [\theta]0 from rest. (a) Write down the Lagrangian and find the equation of motion (b) Show that these equations reduce to those of a simple...

Homework Statement The initial wave function \Psi (x,0) of a free particle is a normalized gaussian with unitary probability. Let \sigma = \Delta x be the initial variance (average of the square deviations) with respect to the position; determine the variance \sigma (t) in a moment later...

The function ax(t) describes the acceleration of a particle moving along the x-axis. At time t = 0, the particle is located at the position x0 and the velocity of the particle is zero. ax(t) = (a0)(e^(-bt)) The numerical values of all parameters are listed below: x0 = 7.10 m a0 =...

The situation I have in my problem is the standard infinite square well from 0 to L. The normalized eigenfunction is \phin(x) = \sqrt{2/L}sin(n\pix/L) for n=1,2,3,... if my wave function at time t=0 is then cos(a)\phi1(x)+sin(a)\phi2(x) is my wave function at more general time t something...

Homework Statement A point mass m is exposed to a time dependent force F(t). Determine the position r(t) of the point mass for the initial conditions r(0) = r_{0}and v(0) = v_{0} Homework Equations The Attempt at a Solution \sumF= ma F_{z}(t) - mg = ma a = 1/m F_{z}(t) - g...

Homework Statement Porous membranes are used to separate mixtures in industry, because smaller compounds permeate through them more easily than larger ones. KnoGas Pty Ltd are trialling an experimental separation process, using a membrane to sep- arate compounds A and B: compound A...

Suppose I have a mechanical system with l + m degrees of freedom and an associated lagrangian L(\alpha,\beta,\dot{\alpha},\dot{\beta},t) where \alpha\in\mathbb{R}^l and \beta\in\mathbb{R}^m. Now suppose I have a known \mathbb{R}^l-valued function f(t) and define a new lagrangian...

Could anyone show me the Baker-Hausdorf formula for product of exponentials in case of operators which are time dependent. I know that there is a time-dependent version of this formula which works under some assumptions are imposed on the operators which appear in exponentials, like e.g...

Homework Statement You have an RC-circuit with emf E, resistance R, and Capacitance C. However, R = R(t) = R_o(t/tao+1)^-1, where R_o is the intitial resistance. Assume that other than the time-dependent resistance, the circuit behaves normally. Homework Equations Show that during...