Consider 1D particle in a box and it’s given normalized wave function Psi = Nsin(bx) where v(x) = 0 outside the box and v(x) = cos(pix/L) inside the box from x = 0 to x = 1. (a) show that the wave function is a valid solution to the Schrödinger equation and what value of b makes it valid? (b) derive the eigenvalue expression

Consider 1D particle in a box and it’s given normalized wave function Psi = Nsin(bx) where v(x) = 0 outside the box and v(x) = cos(pix/L) inside the box from x = 0 to x = 1. (a) show that the wave function is a valid solution to the Schrödinger equation and what value of b makes it valid? (b) derive the eigenvalue expression

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Dielectric Breakdown

A dielectric is a material with low electrical conductivity and so is classified as an insulator. Dielectric materials are used to block the flow of electricity through them, allowing them to behave as an insulators. They can also be used to store electric charge or improve capacitance.Dielectrics have no free electrons for conduction because electrons are tightly bound to the nucleus. Because dielectrics contain a small number of electrons for electrical conductivity, they have a dipole. The two primary roles of dielectrics in electrical devices are insulation and electrical energy storage. An electric field polarizes the dielectric, and the polarization of the molecules allows dielectric materials to store charge.

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Consider 1D particle in a box and it’s given normalized wave function Psi = Nsin(bx) where v(x) = 0 outside the box and v(x) = cos(pix/L) inside the box from x = 0 to x = 1.

(a) show that the wave function is a valid solution to the Schrödinger equation and what value of b makes it valid?

(b) derive the eigenvalue expression

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