The discussion revolves around a problem involving a linear harmonic oscillator, specifically focusing on the potential energy defined as V = (kx^2)/2 and kinetic energy as KE = 1/2 mv^2. The original poster is tasked with using the Heisenberg Uncertainty principle to determine the minimum energy of the system.
Participants are exploring the relationship between energy, position, and momentum uncertainties. There is a suggestion to replace variables with their uncertainties and to minimize the energy expression accordingly. The discussion is ongoing, with no explicit consensus reached yet.
There is an emphasis on the assumptions regarding the uncertainties in momentum and position, which are considered to be greater than the respective uncertainties themselves. The original poster is navigating how to incorporate these assumptions into their calculations.
Doc Al said:Make the (handwaving, but usual) assumption that the momentum must be greater than the uncertainty in momentum, and that the position must be greater than the uncertainty in position. Start by writing the total energy (KE + PE) in terms of those uncertainties. Minimize that to find the lowest allowable energy.