Ground state energy calculations of polynomial potentials based on Hamiltonian moments

Recently, Martin et al calculated approximate energy eigenvalues for potentials of the form V(x) $=$ x$^{a} + \lambda $ x$^{b}$ by use of the multi-point quasi-rotational technique (Rev. Mex. Fis. \textbf{58}, 301 (2012)). In their paper, they considered specific values of $\lambda $ and integer values of $a$ and $b$. In this work, we shall apply a moments approach to study the general ground state energy of such potentials for arbitrary values of $\lambda $ and for integer and non-integer values of $a$ and $b.$ We will compare their results against the generalized moments expansion (GMX) in terms of accuracy and computational effort. In addition, we will calculate the energy spectrum with the Lanczos tridiagonalization technique.