Related papers: Generalization of the Hellmann-Feynman theorem

We discuss the Hellmann-Feynman theorem for degenerate states and its application to the calculation of the derivatives of statistical averages with respect to external parameters.

We revisit the celebrated Hellmann-Feynman theorem (HFT) in the PT invariant non-Hermitian quantum physics framework. We derive a modified version of HFT by changing the definition of inner product and explicitly show that it holds good for…

In this paper we develop the Hellmann-Feynman theorem in statistical mechanics without resorting to the eigenvalues and eigenvectors of the Hamiltonian operator. Present approach does not require the quantum-mechanical version of the…

Using well-known methods we generalize (hyper)virial theorems to case of singular potential. Discussion is carried on for most general second order differential equation, which involves all physically interesting cases, such as…

We introduce a particular nonlinear generalization of quantum mechanics which has the property that it is exactly solvable in terms of the eigenvalues and eigenfunctions of the Hamiltonian of the usual linear quantum mechanics problem. We…

Using well-known methods we generalize (hyper)virial theorems to case of singular potential. Discussion is performed for most general second order differential equation, which involves all physically interesting cases, as Schrodinger and…

Many quantization schemes rely on analogs of classical mechanics where the connections with classical mechanics are indirect. In this work I propose a new and direct connection between classical mechanics and quantum mechanics where the…

A general theory is presented of quantum mechanics of singular, non-autonomous, higher derivative systems. Within that general theory, $n$-th order and $m$-th order Lagrangians are shown to be quantum mechanically equivalent if their…

Hamiltonian mechanics describes the evolution of a system through its Hamiltonian. The Hamiltonian typically also represents the energy observable, a Noether-conserved quantity associated with the time-invariance of the law of evolution. In…

In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…

Using the Hellmann-Feynman theorem, a general comparison theorem is established for an eigenvalue equation of the form $(T+V)|\psi> = E|\psi>$, where $T$ is a kinetic part which depends only on momentums and $V$ is a potential which depends…

The Hamilton-Jacobi theory of Classical Mechanics can be extended in a novel manner to systems which are fuzzy in the sense that they can be represented by wave functions. A constructive interference of the phases of the wave functions then…

We here consider a generalization of the Klein-Gordon scalar wave equation which involves a single arbitrary function. The quantization may be viewed as allowing $\hbar$ to be a function of the momentum or wave vector rather than a…

We present a simple derivation of the Hellmann-Feynman theorem at finite temperature. We illustrate its validity by considering three relevant examples which can be used in quantum mechanics lectures: the one-dimensional harmonic…

We present a derivation of Born's rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantization. Combined to Gleason's theorem, this approach naturally leads to the usual…

Realistic quantum mechanics based on complex probability theory is shown to have a frequency interpretation, to coexist with Bell's theorem, to be linear, to include wavefunctions which are expansions in eigenfunctions of Hermitian…

In this short note we resort to the well known Hellmann-Feynman theorem to prove that some non-relativistic Hamiltonian operators support an infinite number of bound states.

We review the well-known Hellmann Feynman Theorem (HFT), originally developed for Hermitian systems to facilitate the calculation of forces among the molecules. Our work extends this foundational theorem to the domain of non-Hermitian…

We demonstrate that the recently introduced linear equation, reformulating the first Friedmann equation, is the first-order WKB expansion of a quantum cosmological equation. This result shows a deeper underlying connection between General…

We recently introduced a particular nonlinear generalization of quantum mechanics which has the property that it is exactly solvable in terms of the eigenvalues and eigenfunctions of the Hamiltonian of the usual linear quantum mechanics…