I have the following ket in the Fock basis: $\vert3, 0 ,1\rangle$, where each entry defines the number of photons in a particular mode and can take any one of the following numbers: 0, 1, 2, 3. As a result I define the following column vectors $0 = (1, 0, 0, 0)^\text{T}$, $1 = (0, 1, 0, 0)^\text{T}$, $2 = (0, 0, 1, 0)^\text{T}$ and $3 = (0, 0, 0, 1)^\text{T}$, where the superscript $\text{T}$ defines the transpose.
I want to be able to define the ket and associate bra terms to evaluate inner products of the form $\langle\alpha, \beta, \gamma \vert\cdot\vert a, b, c\rangle = \delta_{\alpha a}\delta_{\beta b}\delta_{\gamma c}$. Note that the kets $\langle\alpha, \beta, \gamma\vert$ is the Hermitian conjugate of the corresponding bra $\vert \alpha, \beta, \gamma\rangle$.
How could I implement these inner-products in Mathematica? I imagine that the functions KroneckerProduct
, Transpose
and the KroneckerDelta
would be of use here but I am still unsure. I am aware that there is an add-on for quantum mechanical operations for Mathematica (see this page), but I am sure that this problem does not require this.