Schrodinger Equation n Time dependent Schrodinger equation n

Schrodinger Equation n Time dependent Schrodinger equation : n Hamiltonian for the case of a particle in a fixed potential V(x) : n Given an initial condition , the formal solution :

Plane Wave on a Step Potential n Plane wave incident on a step n General solution for a stationary plane wave where the potential is

Plane Wave on a Step Potential n Wave functions for each side of the step where A : incident wave, B : reflected wave, C : transmitted wave

Plane Wave on a Step Potential n Plane waves incident on a step potential (V=100) where - attenuation - inflection - oscillation

Plane Wave on a Step Potential n Linear superposition of the incident and reflected waves n Interference effect - t=1 : the incident wave is diminished significantly by the reflected wave - t=2 : the system is in anti-phase of the state at t=0

Quantum Scattering 초기화면

Quantum Diffusion n Wave packet propagated in a free space - the wave packet diffuses as time passes

Quantum Diffusion n as a function of lattice position and time - check point : periodic boundary condition - the angle of lines is constant : the wave packet has a constant velocity

Gaussian wave packet on a square potential barrier n n The potential barrier causes a splitting of the wave packet. Tunneling effect

Gaussian wave packet on a square potential barrier n Split of the probability density distribution - check point : the latent probability density inside the potential

Gaussian Wave Packet on a Negative Potential Barrier n check point : the wave function inside the well has a higher frequency

Gaussian Wave Packet on a Negative Potential Barrier n The speed of the packet appears conserved throughout the collision

Gaussian Wave Packet in a Simple Harmonic Oscillator n The particle accelerates from the left hand side and decelerates as it approaches the right.

Gaussian Wave Packet in a Simple Harmonic Oscillator Probability density function shows an excellent sine waves. - check point : tunneling effect n

Gaussian Wave Packet in an Infinite Square Well n The effect of the infinite well : the wave packet is a mess by t=2000 dt

Gaussian Wave Packet in an Infinite Square Well n The particle’s probability distribution diffusing and spreading further and further as time passes. - the packet diffuses and the position becomes less well defined.

참고문헌 n S. Gasiorowicz, Quantum Physics, John Wiley & Sons, Inc. , 1974 n F. J. Blatt, Modern Physics, Mc. Graw-Hill International Editions, 1992 n Related Internet Sites - http: //chriscentral. com - http: // www. mathworks. nl/matlabcentral/fileexchange