Two-dimensional Schrodinger equation

[fkf]

Homework Statement

An ice-hockey puck has the weight 0.170 kg. The ice-hockey rink is 30x60 m. If no players are on the ice, what speed does the puck have due to the quantum effects (ground state)?

Homework Equations

The wave-equation solution to the Schrödinger equation is
ψ(x,y) = Asin(k_x*x)sin(k_y*y)

The Attempt at a Solution

Since we're talking about energies and ground state. I would like to calculate the energy and then the E = mv^2/2 to calculate the speed. But we're in two dimensions and given the solution above

 

[vela]

So what's specifically stopping you?

 

[fkf]

Since the energy is not a vector, I can't threat the energies as vectors and then calculate a given speed for x and y.

 

[vela]

Why would you need to treat E as a vector? Please explain your reasoning on how you're thinking you need to solve this problem fully. Right now, you're just throwing out snippets that don't make sense and make it impossible to figure out what you're thinking.