1. Time independent Schrodinger
wave equation
Dr. Mithil Fal Desai
Shree Mallikarjun and Shri Chetan Manju Desai
College Canacona Goa
Ĥ𝚿 = 𝑬𝚿
2. 𝛙 = wave function
𝐦 = mass
h = plank constant
E = total energy
V = potential energy
Schrodinger time independent wave
equation
𝐝 𝟐
𝛙
𝐝𝐱 𝟐
+
𝐝 𝟐
𝛙
𝐝𝐲 𝟐
+
𝐝 𝟐
𝛙
𝐝𝐳 𝟐
+
𝟖𝛑 𝟐
𝐦
𝐡 𝟐
(𝐄 − 𝐕) = 𝟎
3. Sin (0) = 0
Sin (90) = 1
Sin (x) = y
f(x) = y
Remember f(x)
-1.5
-1
-0.5
0
0.5
1
1.5
0 90 180 270 360 450 540 630 720 810 900
Sine wave
4. -1.5
-1
-0.5
0
0.5
1
1.5
0 90 180 270 360 450 540 630 720 810 900
sinx (dsinx/dx)=cosx d(cosx)/dx =-sinx
Understanding first and second derivative
Difficult?
5. Understanding first and second derivative (easy)
0
20
40
60
80
100
120
0 1 2 3 4 5 6
distance speed
accelaration
Time
Distanc
e
speed acceleration
t x
dx/dt
=speed
d speed/dt=
acceleration
0 0 2 1
1 2 3 2
2 5 5 10
3 10 15 15
4 25 30 20
5 55 50 30
6 105 80 35
7 185 115
8 300
6. Schrodinger wave equation
𝐝 𝟐 𝒇(𝒙)
𝐝𝐱 𝟐 = −
𝟒𝝅 𝟐
λ
𝒇 𝒙
--1
A standing wave having wavelength (λ) that has an
amplitude at any point along x direction is
mathematically described as a function f(x)
7. 𝐝 𝟐ψ
𝐝𝐱 𝟐 = −
𝟒𝝅 𝟐
λ 𝟐 ψ
--2
If a wave function f(x) is represented as 𝝍 (psi) the
equation can be written as
Schrodinger wave equation
8. 𝐝 𝟐 𝛙
𝐝𝐱 𝟐 +
𝐝 𝟐 𝛙
𝐝𝐲 𝟐 +
𝐝 𝟐 𝛙
𝐝𝐳 𝟐 = −
𝟒𝝅 𝟐
λ 𝟐 ψ
--3
When this standing wave is considered in 3 dimensions
having x, y and z coordinates
Schrodinger wave equation
