SCRODINGER EQUATIONS

SCRODINGER EQUATIONS

By

HAISEL MATHEW DEPT. OF PHYSICS

Total energy of a moving particle is equal to sum of its kinetic energy and its potential energy.

) 1 ...(

2

2

m U E  p 

) 2 ....(

...

2

) 1 ...(

2

2

 





m U E p

by sides

both multiply

m U E









 

,

2 2

2





p i

weget x

to respect

with twice

equation this

ate Differenti

Ae

^{Et Px}

i







^{  }

) 3 ...(

2 2

2 2

2 2 2

2 2 2

2

 



 

x p

p p i

x

 

 

 

 









2 ( )

3 ( )

4 ( sin

) 4 ....(

2 2

equ in

and equ

g u

on

t E i

that know

We





 







 







. dim

.

) 5 2

²

...(

2 2

equation r

Schrodinge depedent

time

ensional one

the is

equ This

x U m

i  t  

 



 



 



Three dimensional Time dependent Shrodinger equation

2

2 2 2

2

2 2 2

2 2

2 2

 





 









 

 

 

 

 



 







 



 





 



 here

z U y

x m

i  t 

) 6 ...(

2

2 2

2 2

2 2

 

 





 

 



   

 





 



 







 



 





m U i t

z y

x

 