Final answer:
The function y(x) = A cos kx is not a solution to the stationary Schrödinger equation for the particle in a box.
Step-by-step explanation:
Stationary Schrödinger Equation for a Particle in a Box
The stationary Schrödinger equation for a particle in a box is given by:
d²ψ/dx² + (2mE/ħ²)ψ = 0
where ψ is the wave function, m is the mass of the particle, E is the energy, and ħ is the reduced Planck's constant.
Why the function y(x) = A cos kx is not a solution
For the function y(x) = A cos kx to be a solution to the stationary Schrödinger equation, it needs to satisfy the equation:
d²y/dx² + (2mE/ħ²)y = 0
However, when we differentiate y(x) = A cos kx twice and substitute it into the equation, we will not get a zero value. This means that y(x) = A cos kx is not a solution to the stationary Schrödinger equation for the particle in a box.