Super-Symmetric Quantum Mechanics¶
The idea of supersymmetric quantum mechanics is to introduce a hamiltonian related to supercharge, which is defined through
for all charges \(Q_i\) and
In the 2 charge case, I can define two charges,
The harmonic oscillators can be solved using ladder operators,
This is a hint why we define the charges in that way.
With these charges, we can solve the state that is annihlated by \(Q_1\).
which is the ground state.
The result is