Generalized convexity property for the energy of a quantum-mechanical system

Dependence of the lowest energy level E of a quantum-mechanical system on a parameter lambda is considered for the case when the Hamiltonian is a linear function of lambda: H=T+V+lambdaW, where the operators T, V, and W are homogeneous functions of the particle coordinates of degrees -2, -p and -q, respectively. An inequality is derived which is the generalization of the well-known convexity property of the energy function E(lambda) Examples of application of bounds for the total energy and the electron-nucleus interacticn energies in atoms are given