Suppose an infinite square well extends from -L/2 to +L/2. Solve the time-independent Schrӧdinger’s equation to find the allowed energies and stationary states of a particle with mass m that is confined to this well. Then show that these solutions can be obtained by making the coordinate transformation x’ = x - L/2 for the solutions obtained for the well extending between 0 and L.
Rosanna Cheng PH 106 03.20.17 Pages 644-671 Reading Journal Prediction The chapter will continue to discuss the principles behind light and geometric optics. Notes 23.1 The Ray Model of Light * Light travels in straight lines, making light rays. Light moves from the object to our eyes in straight-line paths, creating the basis of the ray model of light. Rays are extremely narrow beams of light. Although light rays leave each point in many different directions, normally only a small bundle of light rays enter the pupil of an observer’s eye. The ray model explains reflection, refraction, and formation of images by mirrors and lenses. Geometric optics involve straight-line rays at various angles. 23.2 Reflection; Image Formation by a Plane Mirror * Angle of incidence is the angle an incident ray makes with the normal (perpendicular) to the surface. Angle of reflection is the angle the reflected ray makes with the normal. Incident and reflected rays lie in the same plane with the normal to the surface. Reflection angle equals incident angle, says the law of reflection. Diffuse reflection happens when light is incident upon a rough (even microscopically rough) surface and it is reflected in many directions. It is in all directions, meaning an ordinary object can be seen at many different angles by the light reflected from it. Specular reflection is reflection from a mirror. When a narrow beam of light shines on a mirror, the light won’t reach your eye unless your eye is positioned at just the right place where the law of r