Question
In: Physics
Consider the “step” potential: V(x) = 0 if x ≤ 0 = V0 if...
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.
Solutions
genius_generous answered 1 year agoRelated Solutions
Consider the step potential V (x) = 0 x ≤ 0 (I) = V0 x >...
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,...
Bound state in potential. Where V(x)=inf for x<0 V(x)=0 for 0 ≤ x ≤ L V...
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).
We have potential of V (x) = ( 0, 0 ≤ x ≤ a. ∞, elsewhere....
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 delta function potential well :V(x) = −αδ(x) (α > 0). (a) What are the...
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...
The potential in a region between x = 0 and x = 6.00 m is V...
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...
Suppose V and V0 are finitely-generated vector spaces and T : V → V0 is a...
Suppose V and V0 are finitely-generated vector spaces and T : V →
V0 is a linear transformation with ker(T) = {~ 0}. Is it possible
that dim(V ) > dim(V0)? If so, provide a specific example showing
this can occur. Otherwise, provide a general proof showing that we
must have dim(V ) ≤ dim(V0).
The potential of a particle is given as V (x) = -Vδ (x), with V being...
The potential of a particle is given as V (x) = -Vδ (x), with V
being a positive number. Find the wave function and energy of the
bounded states of this particle.
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...
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 potential v(y,z) =sinky(Ce^kz + De^-kz) apply the two boundary conditions a- V(y,z=b)=0 b- V(y=a,z)=0
consider the potential v(y,z) =sinky(Ce^kz + De^-kz)
apply the two boundary conditions
a- V(y,z=b)=0
b- V(y=a,z)=0
1. Consider a free, unbound particle with V (x) = 0 and the initial state wave...
1. Consider a free, unbound particle with V (x) = 0 and the
initial state wave function: Ψ(x, 0) = Ae−a|x| a>0
(a) (3 pts) Normalize the initial state wave function.
(b) (5 pts) Construct Ψ(x, t).
(c) (5 pts) Discuss the limiting cases, i.e. what happens to
position and momentum when a is very small and when a is very
large?
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