#1: Find the time depended wave functions V(x, t) = ?
Related questions
Question
Transcribed Image Text:The system has a particle (its mass is m) in the vacuum, no potential energy (V(x) = 0). The Hamiltonian of the system
ħ² 8²
is given by Ĥ = -2m dx²
The initial wave functions at time t = 0 is
where a is a real constant.
Question #1: Find the time depended wave functions V(x, t) = ?
Question #2: Also, for the wave function (x, t) (that has been found above), find the probability current density
defined as
Note:
+∞
1000
+∞
[too
where ã and ß are complex constants;
v (z,t = 0) = (=) *exp(- 02²)
1
j = 2
2m
8
(¥* (x)pV(x) + V(x) (pV(x))*)
r+∞
88
da exp(-ã+²) = √
dx
dr exp (-ãx² - ikx) =
= √= exp(-1/²)
dk exp
(-²+ ika) = √³ exp(-82²)
4
ax²+bx+c = a (x +
= a (x + 2)² + c - 50
2a
4a
c
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 5 steps with 4 images
