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4.1: Quantum Mechanics Review

4.2: Probability of Finding a Particle
a. mc2 = (h2*c2*32)/(8*E3*L2)
   m = (mc2 value from above)/(3e8)2*(1.602e-19 J)
b. P(x) = XX nm-1 for 6 values of x.
   P(x) = Ψ(x)2, so the value of P(x) will cross the sin wave 2n times.
c. Graph Ψ(x)2 and value for P(x) and find furthest intersection


4.3: Infinite Square Well
En = (hJ2n2/8mL2)/(1.602e-19 J)
&lambdan = 2L/n
a. n=1  ∴  &lambda1=2L
   E1 = (h2/8mL2)*n2
b. n=3  ∴  &lambda1=2L/3
   E3 = E1*n2 = 9*E1
c. n=4  ∴  &lambda1=L/2
   E4 = E1*n2 = 16*E1
d. n=6  ∴  &lambda1=L/3
   E6 = E1*n2 = 36*E1
e. N2L/2=1  ∴  N = sqrt(2/L)


4.4: Finite Square Well
You can copy and paste these.
a. sin(a/2)/exp(-b/2)
b. (pi/2)*(L/a)
c. (-A^2*(2*sin(a/2)*cos(a/2)-a)*L)/(a*2)
d. 1-(-A^2*(2*sin(a/2)*cos(a/2)-a)*L)/(a*2)


NOTE ABOUT HOMEWORK B: THESE ANSWERS MAY NOT BE CORRECT. USE THEM AT YOUR OWN RISK.

HomeworkB 04
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An electron is confined inside a 1-D box with length L.
1) How many antinodes (points with maximum probability density) are there in the n-th energy level of the electron? 
 n antinodes
2) What is the energy of the n-th energy level? 
 En = (hJ2n2/8meL2)/(1.602e-19 J)
3) By what factor does the energy of the n-th level change if L is doubled? 
 En=(h2n2/8m(2L)2)  ∴   by factor = 0.25
4) Use the original L in this question: By what factor does the energy of the 3rd level change if the particle in the box is a muon rather than an electron? The mass of a muon mμ=211me 
 Eμ3/Ee3 = me/mμ = me/211me
5) Consider a wavefunction of a particle in another 1-dimensional well. Choose the appropriate potential that can result in this wave function: 


 If you place U(x) over Ψ then it should be able to rest evenly on top of it.