a) Set up the Schrodinger equation for a particle in an infinite square well where:
V = 0 -a<x<a
V= otherwise
b) Solve the equation to find E and the wave function
a) Set up the Schrodinger equation for a particle in an infinite square well where: V...
help on all a), b), and c) please!! 1. A particle in an infinite square well has an initial wave function Alsin sin 4 0 < x < L otherwise s(x, t = 0) 0 (a) Find A so that the wavefunction is normalized. (b) Find '(z,t). (c) Find the expectation value(E) of the energy of ψ(x,t = 0). You may use the result mx n 2 0 1. A particle in an infinite square well has an initial wave...
2. A particle of mass m in the infinite square well of width a (located at 0 SSa) has as its initial wave function a mixture of two stationary states: v(x,0)Avi(x) +2s (x). (a) Find the probability density of finding the particle at the center of the well, as a function of time. (b) Find the average momentum of the particle at time t.
(15 points) (Straightforward, but part (c) is probably longer) Consider a particle in the infinite square well with the following wavefunction at t 0: V (x,0) 0, otherwise. n(x) is the nth solution to the time independent Schrodinger equation, as discussed in the where class. (a) Find the constant A that will normalize 1, at t-: 0, Will this constant normalize Ψ(x, t) for all time, t (b) Find Ψ(r,t). (c) At time, t-0 find (z), (p), Oz and Op....
Quantum Mechanics question about an infinite square well. A particle in an infinite square well potential has an initial state vector 14() = E1) - %|E2) where E) is the n'th eigenfunctions of the Hamiltonian operator. (a) Find the time evolution of the state vector. (b) Find the expectation value of the position as a function of time.
5) A particle of mass m is in the ground state of the infinite square well 0 < x < a At t-0 the right hand wall suddenly moves to x = 2a, doubling the size of the well. Assume that this expansion happens on a time scale so fast that the initial wave function (at t0+) is the same as just before the expansion (at t-0-) (This is called the "sudden" approximation.) a) What is the probability that a...
A particle in an infinite square well has the initial wave function: (x,0)- A sin(x/a) (0 S a (a) (b) Determine A Find$(z,t) (Hint: You will need to break up this wavefunction into a superposition of pure states. Use orthogonality to find the coefficients.) (c) Calculate (x). Is it a function of time? (d) Calculate (H).
1. Consider a particle of mass m in an infinite square well with potential energy 0 for 0 Sz S a oo otherwise V (x) For simplicity, we may take the 'universe' here to be the region of 0 S z S a, which is where the wave function is nontrivial. Consequently, we may express stationary state n as where En is the associated mechanical energy. It can be shown that () a/2 and (p:)0 for stationary state n. (a)...
Q4. Consider the 1D infinite square-well potential shown in the figure below. V(x) O0 Position (a) State the time-independent Schrödinger equation within the region 0<x<L for a particle with positive energy E 2 marks] (b) The wavefunction for 0<x< L can be written in the general form y(x) = Asin kx + B cos kx. Show that the normalised wavefunction for the 1D infinite potential well becomes 2sn'n? ?snT/where ( "1,2,3 ! where ( n = 1,2,5, ). [4 marks]...
4) A particle in an infinite square well 0 for 0
A NON stationary state A particle of mass m is in an infinite square well potential of width L, as in McIntyre's section 5.4. Suppose we have an initial state vector lv(t -0) results from Mclntrye without re-deriving them, and you may use a computer for your math as long as you include your code in your solution A(3E1) 4iE2)). You may use E. (4 pts) Use a computer to plot this probability density at 4 times: t 0, t2...