1、Schrodingers Wave Equation The wave equation01 Wave function02The wave equationThe one-dimensional, nonrelativistic Schrodingers wave equation（薛定谔波动方程） is given by(x,t) is the wave function，V(x) is the potential function assumed to be independent of time，m is the mass of the particle.),( tx )()( tx
2、= v The left side of Equation is a function of position x only and the right side of the equation is a function of time t only；v Introduce the separation of variables constant Where, E=h=h/2The wave equationTime-independent itemswhere the separation constant is the total energy E of the particle. Eq
3、uation may be written as:where again m is the mass of the particle, V(x) is the potential experienced by the particle, and E is the total energy of the particle. The wave equationWave functionThe wave function is used to describe the behavior of an electron in a crystal，the total wave function is th
4、e product of the position-dependent function and the time-dependent function. ),( txMax Born postulated in 1926 that the function is the probability of finding the particle between x and x + dx at a given time； is a probability density function；dxtx2),( 2),( tx2*2 )()()(),( xxxtx Time-independent pr
5、obability density functionBoundary Conditions（边界条件）2),( txSince the function represents the probability density function, then for a single particle, we must have： 1)( 2 dxxThe wave function and its first derivative must have the following properties if the total energy E and the potential V(x) are finite everywhere：Condition 1 must be finite, single-valued, and continuous；Condition2 must be finite, single-valued, and continuous； )(x xx /)( Wave function
