9) Schrödinger wave equation describes what type of behavior of a particle? 10)

Question

9) Schrödinger wave equation describes what type of behavior of a particle?

10) What two behaviors can occur for a wave impinging on a boundary?

11) To solve Schrödinger wave equation, we need to find a mathematical function (x) that is a solution to the differential equation. To find a specific solution, what else needs to be done to the solution of the equation?

12) Taking the squared absolute amplitude of the wave function allows us to determine what about a particle in a given region of space?

Explanation / Answer

9) Schrödinger wave equation describes wave behavior of a particle.

10) When a wave is incident on boundary, some portion of its energy is transmitted (transmission depend on boundary typa and maybe zero in some cases) while some portion is reflected back. Reflected pulse depends upon the boundary type. If boundary is hard or wave is travelling from rarer medim to denser medium, the reflected wave is inverted with respect to input wave i.e. a 180o phase is added in the reflected wave. If the boundary is soft or wave is travelling from denser medium to rarer medim, reflected wave doesn't have inversion in shape.

11) To solve the specific solution, we need boundary condition on wave function (x).

12) The squared absolute amplitude of the wave function at any point is equal to the probability density of that particle is at that point. So if we integrate this square function over given region of space, we get the probability of particle's position in that region.

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