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

Expert Solution

genius_generous answered 1 year ago

Next > < Previous

Related 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...

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

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?

Consider a particle moving in two spatial dimensions, subject to the following potential: V (x, y)...

Consider a particle moving in two spatial dimensions, subject to the following potential: V (x, y) = ( 0, 0 ≤ x ≤ L & 0 ≤ y ≤ H ∞, otherwise. (a) Write down the time-independent Schr¨odinger equation for this case, and motivate its form. (2) (b) Let k 2 = 2mE/~ 2 and rewrite this equation in a simpler form. (2) (c) Use the method of separation of variables and assume that ψ(x, y) = X(x)Y (y). Rewrite...

Subjects

Question

Consider the “step” potential: ​​​​ V(x) = 0 if x ≤ 0 ​​​​ = V0​​ if...

Solutions

Expert Solution

Related Solutions

Consider the “step” potential: V(x) = 0 if x ≤ 0 = V0 if...