We investigate the problem of a quantum particle confined in a finite one-dimensional square well. The eigenvalues and eigenfunctions are found using a computer algebra system to solve the equations that result from matching the logarithmic derivatives at the well boundaries. The wavefunctions are used to investigate the relation of well depth to tunneling and to the Heisenberg uncertainty relations. We demonstrate how dimensional analysis can be used to locate the minimum uncertainty for a given confining potential.We investigate the problem of a quantum particle confined in a finite one-dimensional square well. The eigenvalues and eigenfunctions are found using a computer algebra system to solve the equations that result from matching the logarithmic derivatives at the well boundaries. The wavefunctions are used to investigate the relation of well depth to tunneling and to the Heisenberg uncertainty relations. We demonstrate how dimensional analysis can be used to locate the minimum uncertainty for a given confining potential.

The Chemical EducatorFeb 1, 20100 citations

A new computing principle

H.A. Fatmi, Germano Resconi

Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento BFeb 1, 198817 citations

Quantum interpolation of polynomials

Daniel M. Kane, Samuel Kutin

Can a quantum computer efficiently interpolate polynomials? We consider black-box algorithms that seek to learn information about a polynomial $f$ from input/output pairs $(x_i, f(x_i))$ . We define a more general class of \emph{ $(d,S)$ -independent} function properties, where, outside of a set $S$ of exceptions, knowing $d$ input values does not help one predict the answer. There are essentially two strategies to computing such a function: query $d+1$ random input values, or search for one of the $|S|$ exceptions. We show that, up to constant factors, we cannot beat these two approaches.Can a quantum computer efficiently interpolate polynomials? We consider black-box algorithms that seek to learn information about a polynomial $f$ from input/output pairs $(x_i, f(x_i))$. We define a more general class of \emph{$(d,S)$-independent} function properties, where, outside of a set $S$ of exceptions, knowing $d$ input values does not help one predict the answer. There are essentially two strategies to computing such a function: query $d+1$ random input values, or search for one of the $|S|$ exceptions. We show that, up to constant factors, we cannot beat these two approaches.

Quantum Information and ComputationJan 1, 20117 citations

Next generation computing

Jim Stikeleather

Cyber Security and Information Intelligence Research WorkshopApr 21, 20103 citations

Einstein’s photon box revisited

Heinz–Jürgen Schmidt

Abstract We present a reformulation of Bohr’s analysis of Einstein’s thought experiment with the photon box, which hopefully settles some unclear issues. The box is weighed by two position measurements, the first immediately before the emission of the photon and the second after a quarter period of oscillation of the box, or alternatively after a half period. These times are precisely defined with respect to the moving clock installed in the box, but vary statistically when measured with a stationary clock outside the box, due to gravitational time dilation in accordance with Bohr’s original idea. Moreover, we will discuss two other proposals to solve the apparent inconsistency without invoking the theory of general relativity.Abstract We present a reformulation of Bohr’s analysis of Einstein’s thought experiment with the photon box, which hopefully settles some unclear issues. The box is weighed by two position measurements, the first immediately before the emission of the photon and the second after a quarter period of oscillation of the box, or alternatively after a half period. These times are precisely defined with respect to the moving clock installed in the box, but vary statistically when measured with a stationary clock outside the box, due to gravitational time dilation in accordance with Bohr’s original idea. Moreover, we will discuss two other proposals to solve the apparent inconsistency without invoking the theory of general relativity.

arXiv:2112.14659International Journal of Theoretical PhysicsJul 21, 20222 citations

Unconventional Computation

Lecture notes in computer scienceJan 1, 200713 citations

Can a quantum computer efficiently interpolate polynomials? We consider black-box algorithms that seek to learn information about a polynomial

f

from input/output pairs

(x_i, f(x_i))

. We define a more general class of \emph{

(d,S)

-independent} function properties, where, outside of a set

S

of exceptions, knowing

d

input values does not help one predict the answer. There are essentially two strategies to computing such a function: query

d+1

random input values, or search for one of the

|S|

exceptions. We show that, up to constant factors, we cannot beat these two approaches.