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1. Consider a particle with mass m in the one dimensional in...

1. Consider a particle with mass m in the one dimensional infinite square well potential with length L. The initial wave function is given by ( ) √ ( ) √ ( ) a) Find the wave function Ψ(x, t) at later time t > 0. b) Calculate the expected value ⟨ ⟩( ) ⟨ ...

2D harmonic oscillator Consider a 2D harmonic oscillator wh...

2D harmonic oscillator Consider a 2D harmonic oscillator which is described by the Hamiltonian = + 2 k (1) where w2 = k/m. (a) Using your knowledge about the 1D harmonic oscillator define operators âr, al and Ni = atai for the 2D harmonic oscillator and argue that you can write the Hamil...

1)( (9 points total) ObservableA Aw =ay normalized eigenst...

1)( (9 points total) ObservableA Aw =ay normalized eigenstates y/ W2 eigenvalues a, a2- ObservableB:Be=bé normalized eigenstates a eigenvalues b.,b, The eigenstates are related by (a) Observable A is measured, and the value ai is found. What is the system's state immediately after meas...

At t=0, a particle is described by the wave function (a) (...

At t=0, a particle is described by the wave function (a) (5 point) Calculate A. (b) (1 point) What is the expression of the momentum operator in momentum space? (c) (3 points) Write down the wave function in the momentum space at t=0. (d) (11 points) Calculate the expectation value of the mo...

(3) For a spinless particle of charge q and mass m in a unif...

(3) For a spinless particle of charge q and mass m in a uniform magnetic induc- tion B0 = Boz, the Hamiltonian is = 2m 1 hV 2 - (4) Choose the magnetic vector potential A to be along y and use separation of variables in Cartesian (rectangular) coordinates to solve the time-independent Schr&oum...

Problem 4 Time-dependent Schrodinger equation is of the for...

Problem 4 Time-dependent Schrodinger equation is of the form d4 a = A4 at Where a is a constant. a. Show that this equation has the following property. Let H be the Hamiltonian of a system composed of two independent parts, so that A(x1,x2) = A1 (x1) + A2(x2) And let the stationary states ...

1 Assume a GaAs quantum well of 20 nm width embedded in a b...

1 Assume a GaAs quantum well of 20 nm width embedded in a barrier material with infinitely high pot ential barrier. We further a%urne th at the GaAs quanturn well is unifo rrnly doped at a dop ing leve! of 1 x 1018 crn- 3 . Let T = O K. (a) Calculat e intr aba nd opt icaJ tra nsition s hetween th...

Consider a cyclotron for accelerating protons to energy 1 Ge...

Consider a cyclotron for accelerating protons to energy 1 GeV. The magnetic field is 2T and the amplitude of the voltage between cylinders is 1 kV a) Estimate the number of orbits needed for protons to become relativistic ( v=1/2c) b) calculate the total number of orbits to reach target energy ...

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