同济大学：《大学物理》课程教学资源（电子教案，英文版）量子3

HEISENBERG DEPT.OF PHYSICS Schrodinger's Equation YOU RRE PROBABL A HERE chase

Schrödinger’s Equation

Agenda today 1.Wave function 2.Schrodinger's equation 3.One dimensional trap 4.Tunnel effect

Agenda today 1. Wave function 2. Schrödinger’s equation 3. One dimensional trap 4. Tunnel effect

Wave function(波函数) What is it really? Guide wave? Wave packet? Density wave?

Wave function(波函数） What is it really? Guide wave? Wave packet? Density wave?

Schrodinger's equation(薛定谔方程)：(1926) 2ΨG,0=[ 7+Uc,ΨG0 Where U is the potential energy for the particle. Laplace operator: 62 idingi. 2+ y2+0z2

Schrodinger’s equation（薛定谔方程）:(1926) ( , )] ( , ) 2 ( , ) [ 2 2 U r t r t m r t t i              Where U is the potential energy for the particle. 2 2 2 2 2 2 2 x y  z          Laplace operator:

Time-independent Schodinger equation: 定态薛定谔方程) V(B--0 2m Where is called time-independent wave function,E is the total energy of the system In one dimensional case d2，2m dx2 (E-0w=0

Time-independent Schodinger equation: 定态薛定谔方程） Where  is called time-independent wave function, E is the total energy of the system In one dimensional case

Born's interpretation:(1928) Like electric field,wave function can satisfy wave equation in quantum physics. Unlike electric field,wave function does not mean anything itself in quantum physics

Born’s interpretation:(1928) Like electric field, wave function can satisfy wave equation in quantum physics. Unlike electric field, wave function does not mean anything itself in quantum physics

Double slits experiment revisited. Electron gun Real pattern The pattern of electron interference is just like that of the light,so we can use a property like E in optics whose square stands for the probability of electron appearing at certain position

Double slits experiment revisited. Electron gun 1 2 I1+ I2 Real pattern The pattern of electron interference is just like that of the light, so we can use a property like E in optics whose square stands for the probability of electron appearing at certain position

But the square of wave function's module is call probability density: If represents a single particle,then is the probability per unit volume that the particle will be found within the infinitesimal volume containing the point. 以牛sd

But the square of wave function’s module is call probability density: If  represents a single particle, then is the probability per unit volume that the particle will be found within the infinitesimal volume containing the point

The property of wave function: Single-valued,limited-valued,continuous. Normalization condition: Ydr=1 Expectation value: x=∫

The property of wave function: Single-valued, limited-valued, continuous. Normalization condition: 1 2     dV Expectation value:

To be,or not to be,that would be the question by Schrodinger's cat Untying the Schrodinger's Cat "It is typical in such a case that an uncertainty initially restricted to an a tomic domain has become transformed into a macroscopic uncertainty which can be resolved through direct observation"Schrodinger

To be, or not to be, that would be the question by Schrodinger’s cat