Related papers: Student Difficulties with Quantum Mechanics Formal…
By a series of simple examples, we illustrate how the lack of mathematical concern can readily lead to surprising mathematical contradictions in wave mechanics. The basic mathematical notions allowing for a precise formulation of the theory…
We investigate the difficulties that undergraduate students in quantum mechanics courses have in transferring learning from previous courses or within the same course from one context to another by administering written tests and conducting…
Classical mechanics, in the Koopman-von Neumann formulation, is described in Hilbert space. It is shown here that classical canonical transformations are generated by Hermitian operators that are in general noncommutative. This naturally…
It is shown that the Schrodinger equation is a byproduct of more deterministic Boltzmann-like equation. All physical information is derived from the solution of this equation, which is a function of space and momentum. The additional terms…
Schroedinger equation on a Hilbert space ${\cal H}$, represents a linear Hamiltonian dynamical system on the space of quantum pure states, the projective Hilbert space $P {\cal H}$. Separable states of a bipartite quantum system form a…
Some aspects of the interpretation of quantum theory are discussed. It is emphasized that quantum theory is formulated in the Cartesian coordinate system; in other coordinates the result obtained with the help of the Hamiltonian formalism…
In this work we present a discussion of the existing links between the procedures of endowing the quantum gravity with a real time and of including in the theory a physical reference frame. More precisely, as first step, we develop the…
Standard quantum mechanics unquestionably violates the separability principle that classical physics (be it point-like analytic, statistical, or field-theoretic) accustomed us to consider as valid. In this paper, quantum nonseparability is…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
The geometry of the symplectic structures and Fubini-Study metric is discussed. Discussion in the paper addresses geometry of Quantum Mechanics in the classical phase space. Also, geometry of Quantum Mechanics in the projective Hilbert…
We present a brief review of physical problems leading to indefinite Hilbert spaces and non-hermitian Hamiltonians. With the exception of pseudo-Riemannian manifolds in GR, the problem of a consistent physical interpretation of these…
We discuss an investigation exploring students' difficulties with equations involving resistance, capacitance and inductance. We find that introductory physics students have great difficulty understanding, e.g., how the resistance of an…
We start to develop the quantization formalism in a hyperbolic Hilbert space. Generalizing Born's probability interpretation, we found that unitary transformations in such a Hilbert space represent a new class of transformations of…
The problem of time in the quantization of gravity arises from the fact that time in Schroedinger's equation is a parameter. This sets time apart from the spatial coordinates, represented by operators in quantum mechanics (QM). Thus "time"…
Useful relations describing arbitrary parameters of given quantum systems can be derived from simple physical constraints imposed on the vectors in the corresponding Hilbert space. This is well known and it usually proceeds by partitioning…
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…
The hilbert-space structure of quantum mechanics is related to the causal structure of space-time. The usual measurement hypotheses apparently preclude nonlinear or stochastic quantum evolution. By admitting a difference in the calculus of…
Geometric (Schrodinger) quantization of nonrelativistic mechanics with respect to different reference frames is considered. In classical nonrelativistic mechanics, a reference frame is represented by a connection on a configuration space…
Courses on undergraduate quantum mechanics usually focus on solutions of the Schr\"odinger equation for several simple one-dimensional examples. When the notion of a Hilbert space is introduced only academic examples are used, such as the…
The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applications to quantum computing. Standard interferomeric techniques are used to construct a physical device capable of universal quantum computation. Some…