# Expectation value of $p^6$ in continuous two-piece symmetric potential wells

## TL;DR

This paper investigates the divergence of the expectation value of $p^6$ in two-piece symmetric potential wells, showing divergence for even states and convergence for odd states, supported by three exactly solvable models.

## Contribution

It demonstrates the state-dependent divergence of $<p^6>$ in two-piece symmetric wells and provides explicit solvable models illustrating this behavior.

## Key findings

- $<p^6>$ diverges for even states in two-piece wells.
- $<p^6>$ converges for odd states in these wells.
- Three exactly solvable models are presented.

## Abstract

Earlier, potentials like square well and several other half-potential wells with discontinuous jump have been found to have the expectation value $<\! p^6 \!>$ to be divergent for all bound states. Here, we consider two-piece symmetric potential wells to prove and demonstrate that in them the expectation value of $p^6$ diverges for even states and converges for odd states. Here, $p$ denotes momentum. We also present three exactly solvable models.