Time evolution Definition and 119 Threads

Suppose I know an initial state \Phi(x)= \exp(-x^2), the Hamiltonian is H = p^2/2m + x^2/2 where p is the mometum operator. If I want to find the time evolution of the state \Phi(x), should I write it as the following? \Psi(x, t) = \exp(-i H t/\hbar)\Phi(x) However, since H contains...

Hello, I am fairly new to quantum physics (I'm actually an engineer, not a physicist). I think I am getting a decent grasp on things, but I have a question. Suppose you have two time dependent states: \Psi_{1} and \Psi_{2}. Also, suppose that we have a constant potential, represented in our...

Homework Statement Suppose the state of a single-mode cavity field is given at time t=0 by |\Psi(0) \rangle = \frac{1}{\sqrt{2}}(|n \rangle + e^{i\phi}|n+1 \rangle) where phi is some phase. Find the state |\psi(t)\rangle at times t > 0. Homework Equations I'm a little...

Hi, I'm trying to derive a wave equation for a gaussian wavepacket for both the position (x) and the momentum (k), for a wave packet of width sigma, at some initial position x0 and with an initial momentum k0. Now I have worked out the initial wavepacket equation to be: psi(x) =...

Hi There, A square pulse of light has the form f(x) = A exp(ik0x) for |x| < L/2 and f(x) = 0 everywhere else. I want to know how that pulse evolves overtime. I want to graph it in Mathematica. I did a Fourier transform to find the wave number spectrum, with the general form: F(k) =...

could we do QM without time evolution ?? that is the idea, could we perform QM without referring to any coordinate called 'time' in the sense that the Hamiltonian and Schroedinguer equation would be H \Psi (x) =0 and time and energy only appear as the pair (p_0 , t) the idea is ...

Homework Statement http://img379.imageshack.us/img379/1864/screenshothw4pdfapplicamd7.png Homework Equations H|\psi > = E_n |\psi > The Attempt at a Solution About part 1 of the question: I can find the eigenfunctions of psi_1 by comparing coefficients with the well known...

Hi, I am trying to calculate the time evolution of a density matrix. Like if there is a mixed state with 50% of |x, 0> and 50% of |y, 0>. After time t due to time evolution, the kets become: |x,t>= e^(-i/h Ht) |x,0> and so on. Is it ok to use these kets instead of the original ket to...

There have been countless discussions about the thought experiment about Schrodinger's cat in a box, and how to describe the state of the cat before and after the box is opened, leading to all sorts of bizarre notions like a half dead/half alive cat inside the box, and I certainly don't fully...

I have a question about the Dirac Equation. I know that if I have a given initial state in non-relativistic quantum mechanics, I can find the Fourier coefficients using that state, and then write down the wavefunction for any time. But if I have an initial state wavefunction (that is, the...

[SOLVED] Calculate time evolution of Schrodinger wave equation Homework Statement At time t=0 particle is in state: \psi\left(x\right)=\sqrt{2}A\phi_{1}(x)+\frac{A}{\sqrt{2}}\phi_{2}(x)+A\phi_{3}(x) where \phi_{n}(x) are eigenfunctions of 1-D infinite potential well. a) Normalize...

Homework Statement At t=0, a given wavefunction is: \left\langle\theta,\phi|\psi(0)\right\rangle = \frac{\imath}{\sqrt{2}}(Y_{1,1}+Y_{1,-1}) Find \left\langle\theta,\phi|\psi(t)\right\rangle. Homework Equations \hat{U}(t)\left|\psi(0)\right\rangle =...

Homework Statement At t=0, the particle is in the eigenstate S_x , which corresponds to the eigenvalues -\hbar \over 2 The particle is in a magnetic field and its Hamiltonian is H=\frac{eB}{mc}S_z . Find the state at t>0. Homework Equations Eigenstate of the Sx is...

Homework Statement Can someone give me a general idea (I do not need and probably will not understand the rigorous mathematics) of how you can use the propagator equation \psi(x,t) = \int{U(x,t;x',t')\psi(x',t')dx'}, the equation for a Gaussian wave packet, \psi(x',0)= e^{i p_0...

What is time evolution? Is it a term only applicabe to matter waves or does it apply to other waves as well?

I'm having some interpretation problems with a rotating dipolar magnetic field, so I need your opinion (I apologise for my bad English). Let there be a magnetic moment "mu" tilted relative to the rotation axis (the "z" axis), with an inclination angle "alpha". The magnetic moment is steadily...

In non-relativistic quantum mechanics time evolution is given by the usual e^{\frac{-i\hat{H}t}{\hbar}} (for non time dependent hamiltonians). How does one time evolve a quantum system in the context of relativity, where time and space have been placed on equal footing? We clearly cannot use...

First year astronomy question, goes as follows: "A closely exact description of the cooling described above is to consider the differential equation which says that rate of charge of thermal energy equals the rate of radiative output. That is: \frac{d}{dt} \frac{\left(3MkT\right)}{m_p} =...

The density operador which describes an ensemble, \rho = \sum_{i} w_i |a_i> <a_i| (represented in the basis in which it is diagonal), evolves in time such that |a_i(t)> = U(t) |a_i> when the enemble remains undisturbed, i.e. the w_i do not change. But for irreversible processes the w_i...