By Professor Dr. Dietrich Stauffer, Professor Dr. Friedrich W. Hehl, Dipl.-Phys. Volker Winkelmann, Professor Dr. John G. Zabolitzky (auth.)
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The Schrodinger equation may be treated by rather similar methods, and all the various techniques and manipulations employed here are common to calculations on quantum -mechanical systems. 8 Literature 1. FORTRAN 77 programming language: any of a very large number of books will do. 2. UNIX operating system: Mark G. Pobell, A Practical Guide to UNIX System V. Any other book on Unix will do as well. 3. Handbooks and Manuals coming with your computer, in particular Users Guides and Language Reference Manuals.
Of course, in both cases, the masses entering the problem are the sum of internal 50 string mass plus any loading masses. In the case of static load, however, we neglected the string mass with respect to the load mass. In string vibration problems, there is usually no external load mass applied to the string. In principle, to be rigorous, both mass densities (J' and p are identical and equal to the sum of string and load mass. , (52) so that dx cancels out. This is the wave equation known from many other problems in physics.
T/hh c a is off-diagonal, b is diagonal matrix element c c factorize matrix gamold=O. s. g=10. totm=O. do 3 i=1,n r(i)=g*rm(i) 3 totm=totm+rm(i) write (*,*) 'totm=',totm*h c c solve linear systems zold=O. do 4 i=1,n z(i)=(r(i)-a*zold)/bet(i) 4 zold=z(i) uold=O. 7 Dynamics of Strings In the last section we balanced the restoring forces due to string tension by static (gravitational) load forces. Let us now consider the motion of a string in time. Assuming some initial displacement u(x, t = 0), what is the configuration u(x, t) of the string at time t?