There are a few problems -
   The Operator has been represented in such a way that for it to act on 
bra/ket we have to use (*). 
    Instead we can define Operator as a function where we pass the bra/ket 
.This function can store the values (for calculation) and then we can print 
the notation too in its symbolic form.
e.g. def Operator( n,m):   #pass the states

     Next problem is when we cant represent an Operator with a superscript 
form( Atleast I havent figured out yet)
    e.g   right = (Bra('m')*(H**2)*Ket('n'))/(E**n - E**m) 

<m|(H)2|n>−Em+En


 represents it as (H) to the power 2(actually evaluates) instead of 
superscript which a Symbol does( In this case I took 'E' as symbol just for 
representation)
If I take 'H' as a symbol, it takes 'H' out of the bra/ket notation( 
assumes as constant) 

So we can define an Operator as:
def Operator(Name, n, m): #Name as a symbolic notation of Operator, n= 
subscript, m = superscript)
We store them for integration of the wavefunction as well as finally print 
it out in the actual notation form.

@Brian @Ondrej Sir, please elaborate on how to go forward with this.     
            

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