Abstract
The Schrodinger equation of a particle moving in one dimension in a given static potential is solved. The density matrix corresponds to a Laplace transform of Green's function and satisfies a diffusion-type equation whlch may be regarded as representing a certain limit of a discrete Markoffian random walk process. The space occupied by the system is divided into nonoverlapping regions; in each, the Sehrodinger equation can be solved. A path concept is introduced to synthesrze the solutions for the regions and formulate the one- particle Green's function. The energy bands of a one-dimensional infinite system are discussed. The condition for the existence of the impurity band is derived, which qualitatively supports Anderson's theory on the absence of diffusion in certain random lattices.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
