Table of Contents
Normalize
for a wavefunction psi the method Normalize() will change the overall prefactor of the wavefunction such that $\langle \psi | \psi \rangle=1$.
Example
We can define the following function: $$ |\psi\rangle = \left(a^{\dagger}_0 a^{\dagger}_1 + a^{\dagger}_0 a^{\dagger}_2 + (1+I) a^{\dagger}_1 a^{\dagger}_2 \right)|0\rangle. $$ after normalization it becomes $$ |\psi\rangle = \left(\frac{1}{\sqrt{4}} a^{\dagger}_0 a^{\dagger}_1 + \frac{1}{\sqrt{4}} a^{\dagger}_0 a^{\dagger}_2 + (1+I)\frac{1}{\sqrt{4}} a^{\dagger}_1 a^{\dagger}_2 \right)|0\rangle. $$
Input
- Example.Quanty
NF=3 NB=0 psi = NewWavefunction(NF, NB, {{"110",1},{"101",1},{"011",(1+I)}}) print(psi) print("The norm of psi is ",psi*psi) psi.Normalize() print(psi) print("The norm of psi is ",psi*psi)
Result
WaveFunction: Wave Function QComplex = 1 (Real==0 or Complex==1) N = 3 (Number of basis functions used to discribe psi) NFermionic modes = 3 (Number of fermions in the one particle basis) NBosonic modes = 0 (Number of bosons in the one particle basis) # pre-factor +I pre-factor Determinant 1 1.000000000000E+00 0.000000000000E+00 110 2 1.000000000000E+00 0.000000000000E+00 101 3 1.000000000000E+00 1.000000000000E+00 011 The norm of psi is 4 WaveFunction: Wave Function QComplex = 1 (Real==0 or Complex==1) N = 3 (Number of basis functions used to discribe psi) NFermionic modes = 3 (Number of fermions in the one particle basis) NBosonic modes = 0 (Number of bosons in the one particle basis) # pre-factor +I pre-factor Determinant 1 5.000000000000E-01 0.000000000000E+00 110 2 5.000000000000E-01 0.000000000000E+00 101 3 5.000000000000E-01 5.000000000000E-01 011 The norm of psi is 1
