A Ladder Operator Solution to the Particle in a Box Problem

A ladder operator solution to the particle in a box problem of elementary quantum mechanics is presented, although the pedagogical use of this method for this problem is questioned.

Input Aggregation in Models of Data Envelopment Analysis: A Statistical Test with an Application to Indian Manufacturing

A problem frequently encountered in Data Envelopment Analysis (DEA) is that the total number of inputs and outputs included tend to be too many relative to the sample size. One way to counter this problem is to combine several inputs (or outputs) into (meaningful) aggregate variables reducing thereby the dimension of the input (or output) vector. A direct effect of input aggregation is to reduce the number of constraints. This, in its turn, alters the optimal value of the objective function. In this paper, we show how a statistical test proposed by Banker (1993) may be applied to test the validity of a specific way of aggregating several inputs. An empirical application using data from Indian manufacturing for the year 2002-03 is included as an example of the proposed test.