Wave Trapped in a Cubic Microwave Cavity: Calculating Lowest Frequency and Modes

[hal2010]

Homework Statement

Consider a cubic microwave cavity one foot on a side. Call this length a for purposes of your calculation. Look for the lowest fre- quency a wave trapped in the cavity can have. How many different modes are there which have this frequency? Assume the surfaces of the cavity all are perfect conductors, implying the conditions that parallel components of E⃗ and perpendicular components of B⃗ vanish at the surface. Estimate the maximum amplitude of E⃗ in volts per meter, such that exactly one photon is present in the cavity.

Homework Equations

The Attempt at a Solution

I looked into the particle in the infinite well and saw some similarities. However with this problem, it appears that there is a single wave function. However, I'm really stuck on how to determine the lowest frequency, and how many modes occupy it.

 

[nickjer]

You don't need quantum mechanics to solve this. This is just an E&M boundary condition problem.