Quantum Harmonic Oscillator Algebra in Sympy

This is kind of garbage, but it does work.

from sympy import *
a = Symbol('a', commutative=False)
adag = Symbol('adag', commutative=False)
ket = Symbol('|0>', commutative=False)
bra = Symbol('<0|', commutative=False)

expr = bra * a * a * a * adag  * adag * adag * ket
print expr
rules = [(a * adag, adag * a + 1), (a * ket, 0), (bra*adag, 0), (bra * ket, 1)]
expr22 =  expr.subs(rules).expand()

for i in range(10):
    expr22 = expr22.expand()
    expr22 = expr22.subs(rules)
print expr22

Need to loop over it because the substitution rules aren’t smart enough to distribute the commutators themselves.

Still, seems to work. Kind of a hack, but seems to work.


Here’s the same thing built out of not much. Not elegantly done particularly

def evalexpr(expr):
    if expr == []:
        return 1
    if expr[-1]=='a':
        return 0
    elif expr[0]=='adag':
        return 0
        for i in range(len(expr)-1):
            if expr[i]=='a' and expr[i+1]=='adag':
                head = expr[0:i]
                if i+2 < len(expr):
                    tail = expr[i+2:]
                    tail = []
                return evalexpr(head+tail) + evalexpr(head+['adag','a']+tail)

print evalexpr(['a','a','a', 'adag', 'adag','adag'])




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