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?
1) A)State the domains (note: [0,inf) for including 0, (0,inf) not
include 0) of the following functions (cannot divide by 0 and
cannot square root negative). B) state which function below is
linear?
a)
g(x)= 1-x
b)h(?)=?−1h(x)=√(x^
-1)
c)?(?)=−1−?1−?f(x)=-(1-x)/√(1-x)
when c does not equal d
simplify
?2−?2?−?=(c^2-d^2)/(c-d)=
(c^2-d^2)/(c-d)=
Consider the “step” potential:
V(x) = 0 if x ≤ 0
= V0 if x ≥ 0
(a) Calculate the reflection coefficient for the case E <
V0 , and (b) for the case E > V0.
We have potential of
V (x) = ( 0, 0 ≤ x ≤ a.
∞, elsewhere.
a) Find the ground state energy and the first and second excited
states, if an electron is enclosed in this potential of size a =
0.100 nm.
b) Find the ground state energy and the first and second excited
states, if a 1 g metal sphere is enclosed in this potential of size
a = 10.0 cm.
c) Are the quantum effects important for...
Consider the potential well defined by
V(x)= {0 -L/2<x<L/2}
{Vo x>L/2 or x<L/2}
1. For E>Vo (unbound state, find the solutions to the
time-independent Schroedinger equation for a particle incident from
the left and traveling to the right(Use boundary conditions to
evaluate coefficients A-F)
2. Find expressions for the transmission and reflection as a
function of energy.
3. Find the necessary conditions for perfect transmission.
Interpret this condition on physical grounds (note that
k=2pi/gamma, which reflects the wave vector ,k,...
Consider the step potential
V (x) = 0 x ≤ 0 (I)
= V0 x > 0 (II) .
(a) What does the wave function for the scattering problem with 0
< E < V0 look like in regions I and II? (Write the equation
for the wave functions, including only terms with non-zero
coefficients.)
(b) What are the boundary conditions for the wave function and its
derivative at x = 0? Define constants you are using (e.g., κ, k,...
The potential in a region between x = 0 and x
= 6.00 m is V = a + bx, where a
= 12.6 V and b = -7.90 V/m.
(a) Determine the potential at x = 0.
______ V
Determine the potential at x = 3.00 m.
______ V
Determine the potential at x = 6.00 m.
______ V
(b) Determine the magnitude and direction of the electric field at
x = 0.
magnitude
________ V/m
direction
+x or...
Consider the delta function potential well :V(x) = −αδ(x) (α
> 0).
(a) What are the boundary conditions on the bound state wave
function and its derivative at x = ±∞ and x = 0? Explain. Hint: You
may find the property stated in Prob. 2 useful.
(b) Show that there is only one bound state.
(c) Find the energy E and wave function ψ(x) of the bound
state.
(d) Find the transmission coefficient for scattering states,
with energy E...