I want to solve Schrödinger's equation with the potential $$V(x)=\frac{1}{2}mx^2+\lambda x$$ algebraically? Is there any way to construct ladder operators that are similar to the one for the harmonic oscillator in order to get the full Hamiltonian written as $H=k_1(b^*b+k_2)$?
A good reference may be suitable as well.