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, to the wavelength).

Expert Solution

3. Perfect transmittance is when reflectance is zero.

i.e when k1 = k2. Then R = reflectance = 0. And transmittance = 1.

queen_honey_blossom answered 2 years ago

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).

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...

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.

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,...

For particles incident on a step potential with E<Vo, show that T=0 using T+R=1

Consider a semi-infinite square well: U(x)=0 for 0 ≤ x ≤ L, U(x)=U0 for x >...

Consider a semi-infinite square well: U(x)=0 for 0 ≤ x ≤ L, U(x)=U0 for x > L, and U(x) is infinity otherwise. Determine the wavefunction for E < Uo , as far as possible, and obtain the transcendental equation for the allowable energies E. Find the necessary condition(s) on E for the solution to exist.

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...

The potential barrier is defined by V(x) = ((A^2-(x^2)*(b^2))^0.5 where x is less than or equal to...

The potential barrier is defined by V(x) = ((A^2-(x^2)*(b^2))^0.5 where x is less than or equal to A/b. First we want to sketch V(x) Then we run a particle into it wth mass m and energy E (which is less than A). Now that we have run the particle into it we are asked to derive an expression for the probability of penetration in terms of D = E/A and sin (y) = bx/A. Finally, we are to evaluate our expression...

Find the all the bound state energies for the potential V = - Vo

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...

Question