Wavelet packet 平(x.）-小e4()s⑨-8因 (dk set k=ko+ ())5 x-e4ep〔月d =4,(x)e- 2sim{告[x-(保)1]》 x-(架)1
Wavelet packet ( ) ( ) ( ) 0 2 0 2 , d k k k i kx t k k x t e u x k + − − = ( ) ( ) 0 2 0 0 2 d k k k i kx t k k u x e k + − − set 0 k k = + ( ) 0 0 d d k k k + ( ) ( ) ( ) 0 0 0 0 2 2 d , exp d d k k i k x t k k x t u x e i x t k − − = − ( ) ( ) ( ) ( ) 0 0 0 0 0 2 2sin k i k x t k k k d dk d dk x t u x e x t − − = − ( ) ( ) 0 k k u x u x
For the analysis of wave packet movement,only need to analyse 2(that is,the probability distribution). e中沿 (ay set w=x- sin学w dk The wave function centered in the range of △k The center of wave packet 2π 0 2π is:w=0. W △k △k
For the analysis of wave packet movement, only need to analyse 2 (that is, the probability distribution). ( ) ( ) ( ) ( ) ( ) 0 0 0 2 2 2 2 d 2 d d 2 d sin , k k k k k k k x t x t u x k x t − = − set 0 d d k w x t k = − 2 w k 2 k − 0 2 2 2 sin k k w w The wave function centered in the range of , The center of wave packet is : w＝0. 2 k
do There is x= I=. dk E(k)=ho(k) If the wave packet is a quasi-particle,the particle velocity is The width of Brillouin zone:2/a,assume that Ak is small, generally require Ak<2π 2π that is >>a a △k For 3D case,the velocity of electron is: E
There is 0 0 d 1 d d d k k E x t t k k = = If the wave packet is a quasi-particle, the particle velocity is ( ) 0 0 d 1 d d d k x E v k t k = = E k k ( ) = ( ) The width of Brillouin zone: 2/a ，assume that k is small, generally require that is For 3D case, the velocity of electron is: 1 v = k E a k 2 a k 2
For the dispersion of Bloch wave,a stable wave packet requires that the wave vector rangek should be very small. a Considering the uncertainty relation 9,=A≥经Aa suggesting that if the wave packet size is much larger than the cell size,the movement of electrons can be described in terms of wave packet.For transportation,only when the electron mean free path is much larger than the cell size,the electrons in the crystal can be solved as a quasi-classical particle.The motion speed of wave packet (group velocity)is equal to the average velocity of the particles in the center of wave packet
For the dispersion of Bloch wave, a stable wave packet requires that the wave vector range △k should be very small. Considering the uncertainty relation 2 x x = p x k x a k 2 x a suggesting that if the wave packet size is much larger than the cell size, the movement of electrons can be described in terms of wave packet. For transportation, only when the electron mean free path is much larger than the cell size, the electrons in the crystal can be solved as a quasi-classical particle. The motion speed of wave packet (group velocity) is equal to the average velocity of the particles in the center of wave packet