PHY3702 Assignment 2 Solutions 2026

PHY3702 Assignment 2 Solutions 2026
UNISA

DUE DATE: 15 JULY 2026

,PHY3702 Assignment 2 – Complete Solutions BY iQ Level

Question 1

The potential well is
0, 0 < 𝑥 < 𝑎
𝑉(𝑥) = {
∞, elsewhere


(Inside the well the potential must be zero, otherwise bound states do not exist.)



Question 1(a)

: Schrödinger equation

Inside the well:

ℏ2 𝑑 2 𝜓
− = 𝐸𝜓
2𝑚 𝑑𝑥 2


Rearranging:

𝑑2 𝜓
+ 𝑘2𝜓 = 0
𝑑𝑥 2


where
2𝑚𝐸
𝑘2 =
ℏ2


The general solution is

𝜓(𝑥) = 𝐴sin⁡(𝑘𝑥) + 𝐵cos⁡(𝑘𝑥)


Apply boundary conditions

At 𝑥 = 0,

𝜓(0) = 0


therefore

𝐵=0

, Hence

𝜓(𝑥) = 𝐴sin⁡(𝑘𝑥)


At 𝑥 = 𝑎,

𝜓(𝑎) = 0


thus

𝐴sin⁡(𝑘𝑎) = 0


For non-trivial solutions,

sin⁡(𝑘𝑎) = 0


which gives

𝑘𝑎 = 𝑛𝜋


where

𝑛 = 1,2,3, …


Therefore
𝑛𝜋
𝑘𝑛 =
𝑎


Energy levels

Using

ℏ2 𝑘 2
𝐸=
2𝑚
ℏ2 𝑛𝜋 2
𝐸𝑛 = ( )
2𝑚 𝑎


Hence

𝑛 2 𝜋 2 ℏ2
𝐸𝑛 =
2𝑚𝑎2