A particle is bound between x = -L to x = L where L = 0.1...
A particle is bound between x = -L to x = L where L = 0.1 nm.
The wave function is given by:
a) Find A
b) What is the probability of finding the particle between -0.05
nm and 0.05 nm?
Solutions
Expert Solution
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Bound state in potential. Where
V(x)=inf for x<0
V(x)=0 for 0 ≤ x ≤ L
V (x) = U for x > L
Write down the Schrödingerequation and solutions (wavesolutions)
on general form for the three V(x).
1. Consider a particle of mass m in a box of
length L with boundaries at x = 0 and x =
L. At t = 0 the wavefunction is
where A is the normalization constant.
(a) Determine the basis eigen states for a particle in the box.
(b) Determine the normalization constant A.
(c) Determine the probability of finding the particle in the
ground state at t ≠ 0.
(d) Show that the sum of probabilities of finding the...
A 3kg particle moves along the X axis according to X(t) =
6t+3t2+2t3, where X is in meters and t is in
seconds. What net force is acting on it at t = 3 s?
The position of a particle is given in cm by x = (8) cos 9?t,
where t is in seconds. (a) Find the maximum speed.b) Find the
maximum acceleration of the particle.(c) What is the first time
that the particle is at x = 0 and moving in the +x direction?
Let X ∼ Normal(µ, 1).
(a) Give an interval (L, U), where U and L are based on X, such
that P(L < µ < U) = 0.99.
(b) Give an upper bound U based on X such that P(µ < U) =
0.99.
(c) Give a lower bound L based on X such that P(L < µ) =
0.99.
A particle moves with position r(t) =
x(t) i + y(t)
j where x(t) =
10t2 and y(t) = -3t
+ 2, with x and y in meters and t in seconds.
(a) Find the average velocity for the time interval from 1.00 s
to 3.00 s.
(b) Find the instantaneous velocity at t = 1.00 s.
(c) Find the average acceleration from 1.00 s to 3.00 s.
(d) Find the instantaneous acceleration at t = 1.00 s.
Compute the area under y = √x between x = a and x = b where a
and b are user specified values obtained via cin. Account for
invalid user input cases of a < 0 and a > b. For each case of
invalid input, immediately output to the user what the error was.
Allow the user a total of three chances to enter valid input for
each input request. If the user enters incorrect input three times
in...
(a) Prove that there are no degenerate bound states in an
infinite (−∞ < x < ∞) one-dimensional space. That is, if
ψ1(x) and ψ2(x) are two bound-state solutions of − (h^2/2m) (d^2ψ
dx^2) + V (x)ψ = Eψ for the same energy E, it will necessarily
follow that ψ2 = Cψ1, where C is just a constant (linear
dependence). Bound-state solutions should of course vanish at x →
±∞.
(b) Imagine now that our particle is restricted to move...