A particle of mass m in a rectangular box with dimensions x, y, and z has ground state energy

where k is a physical constant. In Exercise 52 of Section 7.3, you were asked to minimize the ground state energy subject to the fixed volume constraint V₀ = xyz using substitution. Solve the same constrained optimization problem using the method of Lagrange multipliers.

Data from Exercise 52 of Section 7.3.

A particle of mass m in a rectangular box with dimensions x, y, and z has ground state energy

where k is a physical constant. If the volume of the box satisfies xyz = V₀ for constant V₀, find the values of x, y, and z that minimize the ground state energy.

Transcribed Image Text:

E(x, y, z) K² 8m 2 + 2