A particle in the infinite square well has as its initial wave function an even mixture...
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*...
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 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).
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...
The particle of mass m in the infinite square well (of width a) starts out of the left half of the well, and is (at 1-0) equally likely to be found at any point in that region, what is the initial wave function Ψ(0)? Assume it is real, do not forget to normalize it.
please show work 1. (5 points) The wave function for a particle in an infinite square well (0<xca) at t-o is given by: (x,0)-Finm). Which one of the following is the wave function at time t? (Clearly circle your choice.) 2 . 3x 2 . 3m (a) (x.1)-Vasin( )cos(Ey/A) 2 . 3tx sies-E/n) (c) Both (a) and (b) above are correct. (d) None of the above.
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.
4) A particle in an infinite square well 0 for 0
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