where φ, ψ ∈ L, H = −~ 2m ∆+V (~x) is essentially self-adjoint, H̄ is the closure ofH , and φ, ψ, V each carries at most a finite number of singularities and discontinuities. In flavor of physics… (More)

Using Nonstandard Analysis, we will provide a rigorous computation for the harmonic oscillator Feynman path integral. The computation will be done without having prior knowledge of the classical… (More)

Abstract. We will derive a rigorous real time propagator for the Non-relativistic Quantum Mechanic L transition probability amplitude and for the Non-relativistic wave function. The propagator will… (More)

Abstract. In this paper, we will show the existence and uniqueness of a real-time, time-sliced Feynman path integral for quantum systems with vector potential. Our formulation of the path integral… (More)

Using nonstandard analysis, we will extend the classical Turing machines into the internal Turing machines. The internal Turing machines have the capability to work with infinite (∗-finite) number of… (More)

The goals of this paper are to show the following. First, Grover’s algorithm can be viewed as a digital approximation to the analog quantum algorithm proposed in ”An Analog Analogue of a Digital… (More)

Abstract. In this paper, we will be concerned with a class of quantum algorithms that contains Shor’s factoring and discrete log algorithms. It turns out that for these algorithms, the probability of… (More)