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 Schrodinger 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.

 

[paranormal]

, the wavefunction ψ is dependent on both x and y coordinates. So, I would first need to determine the values of kx and ky using the dimensions of the rink. Then, I can plug those values into the equation E = ħ^2(kx^2+ky^2)/2m to calculate the energy of the puck in its ground state. From there, I can use the given mass of the puck to calculate its speed using the equation v = √(2E/m). This will give me the speed of the puck due to the quantum effects in the ground state. However, it's important to note that this speed will be incredibly small and likely negligible compared to the speed of the puck in a real ice hockey game. The Schrodinger equation and its solutions are typically used to describe the behavior of particles on a microscopic scale, so it may not accurately predict the behavior of a macroscopic object like a hockey puck on an ice rink. Other factors, such as friction and external forces, would have a much larger impact on the speed of the puck in a real game scenario.