A particle of mass m is subject to a doubly infinite square well, with widths L,...
2. A particle of mass m in the infinite square well of width a at time 1 - 0 has wave function that is an equal weight mixture of the two lowest n= 1,2 energy stationary states: (x,0) - C[4,(x)+42(x)] (a) Normalize the wave function. Hints: 1. Exploit the orthonormality of W, 2. Recall that if a wave function is normalized at t = 0, it stays normalized. (b) Find '(x, t) and (x,1)1at a later time 1>0. Express Y*...
I. Consider a particle in an infinite square well potential with sides at x = ±a. Find the expectation value of the operator given below in any eigenstate of the particle: I. Consider a particle in an infinite square well potential with sides at x = ±a. Find the expectation value of the operator given below in any eigenstate of the particle:
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.
please explain all, thanks! 4. (60 pts) A particle in an infinite square well of width L has an initial wave function (x,t = 0) = Ax(L - x)2, OSX SL a) Find y(x, t) fort > 0. You first have to normalize the wave function. Hint: this is best expressed an infinite series: show that the wave function coefficients are on = * 31% (12 – n?)(1-(-1)") → (n = 87315 (12 - nºre?); n odd. b) Which energy...
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.
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...
6. (Extra Credit: 6 Points) Consider two noninteracting particles of mass m in an infinite square well of width L. For the case with one particle in the single-particle state In) and the other in the state k) (nメk), calculate the expectation value of the squared inter-particle spacing (71-72) , assuming (a) the particles are distinguishable, (b) the particles are identical in a symmetrical spatial state, and (c) the particles are identical in an anti-symmetric spatial state. Use Dirac notation...
[12 6. Consid er a particle of mass m moving in an infinitely deep square well potential of width a, whose wave function at time t 0 is where on Ce) is the normaized wave function of the n-th eigenstate of the Hamitonian of that particle The corresponding eigen-energy of the n-th state is 2ma?n 1,2,3,... (e) Find the average energy of the system (ie. the expectation value () (b) Write down the wave function p(z,t) at a later 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...