Related papers: Correct form of the electron wavefunction in perio…
Stationary-state Schr{\"o}dinger-Pauli theory is a description of electrons with a spin moment in an external electromagnetic field. For 2-electron systems as described by the Schr{\"o}dinger-Pauli theory Hamiltonian with a symmetrical…
The problem of interest in this article are waves on a layer of finite depth governed by the Euler equations in the presence of gravity, surface tension, and vertical electric fields. Perturbation theory is used to identify canonical…
High-energy electrons that are used as a probe of specimens in transmission electron microscopy exhibit a complex and rich behavior due to multiple scattering. Among other things, understanding the dynamical effects is needed for a…
A new variational technique is developed to investigate the polaronic features of the Holstein Molecular Crystal Model. It is based on a linear superposition of Bloch states that describe large and small polaron wave functions. It is shown…
Due to the space and time dependence of the wave function in the time dependent Schroedinger equation, different boundary conditions are possible. The equation is usually solved as an ``initial value problem'', by fixing the value of the…
Wavefunctions for large electron numbers $N$ are plagued by the Exponential Wall Problem (EWP), i.e., an exponential increase in the dimensions of Hilbert space with $N$. Therefore they loose their meaning for macroscopic systems, a point…
We show that equation for radial wave function in its traditional form is compatible with the full Schrodinger equation if and only if a definite additional constraint required. This constraint has a boundary condition form at the origin.…
In the one-dimensional periodic potential case, we formulate the condition of Bloch periodicity for the reduced action by using the relation between the wave function and the reduced action established in the context of the equivalence…
Electronic band structure for electrons bound on periodic minimal surfaces is differential-geometrically formulated and numerically calculated. We focus on minimal surfaces because they are not only mathematically elegant (with the surface…
In solid state conductors, linear response to a steady electric field is normally dominated by Bloch state occupation number changes that are correlated with group velocity and lead to a steady state current. However, for a number of…
With a generic lattice model for electrons occupying a semi-infinite crystal with a hard surface, we study the eigenstates of the system with a bulk band gap (or the gap with nodal points). The exact solution to the wave functions of…
A de Broglie-Bohm like model of Dirac equation, that leads to the correct Pauli equations for electrons and positrons in the low-speed limit, is presented. Under this theoretical framework, that affords an interpretation of the quantum…
In this paper I present a thought experiment that gives different results depending on whether or not the wavefunction collapses. Since the wavefunction does not obey the Schrodinger equation during the collapse, conservation laws are…
Liouville's theorem on the conservation of phase space volume is violated by Berry phase in the semiclassical dynamics of Bloch electrons. This leads to a modification of the phase space density of states, whose significance is discussed in…
A novel Bloch-waves based one-step theory of photoemission is developed within the augmented plane wave formalism. Implications of multi-Bloch-wave structure of photoelectron final states for band mapping are established. Interference…
By introducing concepts of beam shaping into quantum mechanics, we show how interference effects of the quantum wavefunction describing multiple electrons can exactly balance the repulsion among the electrons. With proper shaping of the…
Periodic structures are ubiquitous in quantum many-body systems and quantum field theories, ranging from lattice models, compact spaces, to topological phenomena. However, previous bootstrap studies encountered technical challenges even for…
We systematically apply the Born-Oppenheimer approximation to show that the Migdal effect in a solid crystal is entirely due to non-adiabatic effects, namely the deviation of the wave function from exact factorization of the electronic and…
It is shown that von Neumann-Landau equation for wave functions can present a mathematical formalism of motion of quantum mechanics. The wave functions of von Neumann-Landau equation for a single particle are `bipartite', in which the…
The microscopic wave functions of the composite fermion theory can incorporate electron mass anisotropy by a trivial rescaling of the coordinates. These wave functions are very likely adiabatically connected to the actual wave functions of…