The Schrodinger equation is effectively the classical wave equation recast to account for matter waves by...

The Schrodinger equation is effectively the classical wave equation recast to account for matter waves by using the deBroglie relation. The simplest possible application of the Schrodinger equation is the so-called free particle system where potential energy, V(x)=0.
a) Show that plane waves, such as , are solutions (k is the wavevector).
b) Use your solution above to find the energy of a free particle.
c) What values are possible for position, x, and momentum, p.

Expert Solution

Plane wave solution of Schrondinger euation for free article are not a physically acceptable solution because plane wave is spread out in whole space.

Physically acceptable solution of Schrondinger euation for free article is best represented by wave packet which is a linear superposition of plane waves.

genius_generous answered 2 years ago

What are Matter (de Broglie) Waves? If matter has a wave nature, why is this wave-like...

What are Matter (de Broglie) Waves? If matter has a wave nature, why is this wave-like characteristic not observable in our daily experiences? How can matter have a dual wave-particle nature?

Derive the classical wave equation. Describe the relationship between classical wave equation and electromagnetic equations.

derive the classical wave equation. Show the relationship between this equation and the electromagnetic wave equation.

Use the Schrodinger equation solution of the H atom corresponding to its wave function for the...

Use the Schrodinger equation solution of the H atom corresponding to its wave function for the 3dxy orbital to explain why this orbital has no radial node. Questions to consider: (j) What is the value of the wave function and thus the radial part of the function at a node? (ii) What factor of the radial part of the wave function, containing r, can equal your value in (i) and thus allow you to obtain a value for r?

Extract the radial part of the Schrodinger. wave equation in spherical coordinates for a hydrogen like...

Extract the radial part of the Schrodinger. wave equation in spherical coordinates for a hydrogen like atom. Use the methods of eigenvalues. Plot the results with the radial wave function as a function of the distance from the nucleus r.

Determine the Time-Dependent Schrodinger Equation (TDSE) from the classical non-relativistic expression for the energy of a...

Determine the Time-Dependent Schrodinger Equation (TDSE) from the classical non-relativistic expression for the energy of a particle and de Broglie’s claim that all particles can be represented as waves. (Important: Describe as much as possible and must use your own words to explain it.)

Analysis of waves in shallow water (depth much less than wavelength) yields te following wave equation:...

Analysis of waves in shallow water (depth much less than wavelength) yields te following wave equation: where h is the water depth and gthe gravitational acceleration. Give an expression for the wave speed.

write the Hamiltonian, the Green's function and the Schrodinger equation in spherical coordinates

If matter has a wave nature, why is this wave-like characteristic not observable in our daily...

If matter has a wave nature, why is this wave-like characteristic not observable in our daily experiences? Any object of macroscopic size—including a grain of dust—has an undetectably small wavelength, so any diffraction effects it might exhibit are very small, effectively undetectable. Recall historically how the diffraction of sound waves was at one time well known, but the diffraction of light was not. Only objects of macroscopic size, like an ocean wave, actually exhibit a wave nature. Smaller, microscopic objects—including...

Solve the time independent schrodinger equation for a particle confined to a mobius strip.

Question