1. Consider a particle with mass m and the wave function psi(x) = B * e ^ (- d|x|) where B and d are two real constants.
Posted: Tue Jul 12, 2022 1:35 pm
1. Consider a particle with mass m and the wave function psi(x) = B * e ^ (- d|x|) where B and d are two real constants.
a) By normalizing this wave function find the unknown constant B.
b) Find the portability of finding particle in the region |x| < 5 .
c) Calculate the expectation value of position operator, langlexrangle=?
d) Calculate the expectation value of langlex ^ 2rangle=?
e) Calculate the expectation value of the momentum operator, langleprangle=?
f) If assume that this wave function is at time t = 0 is an stationary state of a given Hamiltonian with energy E = - E_{0} i.e., psi(x, t = 0) = B * e ^ (- d|x|) What is the solution of the Schrödinger equation at time t > 0
Hint: f(x|)=\ matrix f(x),\\f(- x), matrix for x > 0 for x<0^ prime
a) By normalizing this wave function find the unknown constant B.
b) Find the portability of finding particle in the region |x| < 5 .
c) Calculate the expectation value of position operator, langlexrangle=?
d) Calculate the expectation value of langlex ^ 2rangle=?
e) Calculate the expectation value of the momentum operator, langleprangle=?
f) If assume that this wave function is at time t = 0 is an stationary state of a given Hamiltonian with energy E = - E_{0} i.e., psi(x, t = 0) = B * e ^ (- d|x|) What is the solution of the Schrödinger equation at time t > 0
Hint: f(x|)=\ matrix f(x),\\f(- x), matrix for x > 0 for x<0^ prime