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for a one dimensional particle in a box, write an integral expression for the average value,...
1. For the one-dimensional particle in a box of length L=1A a. Write an integral expression for the probability of finding the particle between L/4 and L/3, for the fourth excited state. b. Write the wavefunction for the fourth excited state c. Calculate the numerical probability of finding the particle between 0 and L/3, for the ground state. I am having trouble understanding these questions for my practice assignment, I have an exam tonight and I want to be able...
64 Consider a particle in a one-dimensional box in the ground state v, and the first excited state , described by the wave functions listed below. For each wave function, calculate the expec- tation value of the position (x), the expectation value of the position squared (), the expecta- tion value of the momentum (p), and the expectation value of the momentum squared (p2). 2 . 2x Ossa 0sxSa (b) Y2(x) = Vasin-
4. A (one dimensional) particle in a box of length 2a (i.e., zero potential energy) is represented by the wavefunction v(x) 0, otherwise a. Sketch the wavefunction. Write down the (time independent) Schrodinger equation. Show whether or not the wavefunction is a solution to the equation. b. What does it mean physically if the wavefunction of the particle is NOT a solution to the Schrodinger equation? Explain. c. Determine the normalization constant A. 5. Same system. Find the average or...
help Part B. Open questions. 1. (30 points) For the one-dimensional particle in a box of length L. a. Write the wavefunction for the fifth excited state b. Calculate the energy for the fifth excited state when L = 18 and m = Ing. c. Write an integral expression for the probability of finding the particle between L/4 and L/2, for the second excited state. d. Calculate the numerical probability of finding the particle between 0 and L15, for the...
2. (a) Are the eigenfunctions of H for the particle in the one-dimensional box also eigenfunctions of the position operator ? (b) Calculate the average value of x for the case where n 4. Explain your result by comparing it with what you would expect for a classical particle. Repeat your calculation for n = 6 and, from these two results, suggest an expression valid for all values of n. How does your result compare with the prediction based on...
for a particle in a one dimensional box of length L if the particle is on the n=4 state what is the probability of finding the particle within a) 0<x<5L/6 b) L/4<x<L/2 c) 5L/6<x<L
For the one-dimensional particle in a box of length L = 1 Å, what will be the energy of the ground state? a. Write Schrodinger’s equation for if the potential between 0 and L is zero b. Write Schrodinger’s equation for if the potential between 0 and L has a constant value of V_o
/a). The wavefunction for a particle in a one-dimensional box of length a is v = (2)"sin(n What is the probability of finding the particle in the middle third of the box for n = 2?
nh 61. The energy for one-dimensional particle-in-a-box is E=" 1. For a particle in a 0 three-dimensional cubic box (Lx=Ly=L2), if an energy level has twice the energy of the ground state, what is the degeneracy of this energy level? (B) 1 (C)2 (D) 3 (E) 4 (A) 0
5 Suppose that a particle in a 1-dimensional box is in the state (x) = NxL-x) OSxSL = 0 everywhere else a) Show that this wavefunction is not an eigenvalue of the Hamiltonian operator. b) Sketch the wavefunction (x) c) Determine the value of the normalization constant N ! What this means is that the state is not stationary. so it evolves in time according to the full time-dependent Schrodinger equation. The expression given for (x) represents one instant in...