A variational method is studied based on the minimum of energy variance. The method is tested on exactly soluble problems in quantum mechanics, and is shown to be a useful tool whenever the properties of states are more relevant than the eigenvalues. In quantum field theory the method provides a consistent second order extension of the gaussian effective potential. Typeset using REVTEX

We show that there exist spurious states for the sector two tensor Hamiltonian in multidimensional supersymmetric quantum mechanics. For one-dimensional supersymmetric quantum mechanics on an infinite domain, the sector one and two Hamiltonians have identical spectra with the exception of the ground state of the sector one. For tensorial multidimensional supersymmetric quantum mechanics, there ...

Generation of exactly solvable quantum systems in non-relativistic quantum mechanics from an already analytically solved quantum system is presented using extended transformation method. The bound state quantized energy spectra and the corresponding wavefunctions of the generated potentials are obtained. It is also shown that eigenfunctions of the new quantum systems can easily be normalized. c...

Preface This is a draft of an upcoming book with a computational approach to quantum mechanics based viewing the the Schrödinger equation for a many-electron atom or molecule as a non-linear system of of one-electron equations in the spirit of Hartrees classical method, which is solved in a collective computational process with each electron updating its own three-dimensional wave function acco...

Quantum Hamilton-Jacobi Theory and supersymmetric quantum mechanics (SUSYQM) are two parallel methods to determine the spectra of a quantum mechanical systems without solving the Schrödinger equation. In a previous paper [1], it was shown that the shape invariance, which is an integrability condition in SUSYQM formalism, can be utilized to develop an iterative algorithm to determine the quantum...

the controversial theories of modern physics created a remarkable revolution in twentieth-century literature. the progressive novelists of the century, inspired by the concepts in quantum mechanics, expressed the concerns of living in the modern world in the form of non-linear, heterogeneous writing based on doubt. in his autobiographical work, entitled w or the childhood memory, george perec p...

Quantum statistical mechanics is statistical mechanics applied to quantum mechanical systems. In quantum mechanics a statistical ensemble (probability distribution over possiblequantum states) is described by a density operatorS, which is a nonnegative, self-adjoint, trace-classoperator of trace 1 on the Hilbert space Hdescribing the quantum system. This can be shown under various mathematical ...

Starting from a naive investigation into the nature of experiments on a physical system one can argue that states of the system should pair nondegenerately with physical observables. This duality is closely related to that between space and quantity, or, geometry and algebra. In particular, it is grounded in the mathematical framework of both classical and quantum mechanics in the form of a pai...

We generalize the ZX calculus to quantum systems of dimension higher than two. The resulting calculus is sound and universal for quantum mechanics. We define the notion of a mutually unbiased qudit theory and study two particular instances of these theories in detail: qudit stabilizer quantum mechanics and Spekkens-Schreiber toy theory for dits. The calculus allows us to analyze the structure o...