DECLARE SUB Pict1 ()
DECLARE SUB Pict2 ()
DECLARE SUB Pict3 ()
DECLARE SUB Pager ()
DECLARE SUB Askn (n!)
10 REM GE copeland                                              
REM Dept of Physics
REM Old Dominion University
REM Norfolk VA 23504
REM 3/23/2001
REM
PRINT CHR$(12)
PRINT "Summerfeld Orbits for Hydrogenic systems"

        CALL Pict1
        CALL Pager
        CALL Pict2
        CALL Pager
        CALL Pict3
        CALL Askn(n)
        CALL Pager

360 PRINT "Please input the nuclear charge and mass (Z and M (in AMU))";
370 INPUT z, m
380 m1 = 1! / 1830!
390 REM this is the electron mass                                  
400 r0 = .529
REM bohr radius in angstroms units                  
410 REM a=r0*n^2/z    and b=r0*n*k/z-----hertzberg p18             
420 u = (m * m1) / (m + m1)
421 REM u not used......                                           
422 PRINT "There will be "; n; " orbits calculated"
640 REM                                                            
2000 REM calculation subroutine                                   
REM Determine the number of points that will be plotted
REM
p = 0
   a = r0 * n * n / z
 FOR x = -a TO a STEP a / 50
        p = p + 1
 NEXT x
 FOR x = a - a / 50 TO -a STEP -a / 50
        p = p + 1
 NEXT x

2010 OPEN "plttek.dat" FOR OUTPUT AS #2
2021 PRINT #2, 1
2022 PRINT #2, n
2030 PRINT #2, p
2040 PRINT #2, "Distance <Bohrs>"
2041 PRINT #2, "Distance <Bohrs>"
2070 PRINT #2, "Summerfeld orbits for n="; n; "k=1,,,n and z="; z
2080 PRINT #2, "Reduced mass ="; u; " amu"
2100 REM calculate                                                 
PRINT "k          Semi-major    Semi-minor  Eccentricity"
PRINT "           Axis(A)       Axis(A)"
2110 FOR k = n TO 1 STEP -1

2140 a = r0 * n * n / z
2150 b = r0 * n * k / z
ecc = SQR(1 - (b / a) ^ 2)
  PRINT k, a, b, ecc
2200 FOR x = -a TO a STEP a / 50

2210 y = b * SQR(1 - x * x / (a * a))
2230 PRINT #2, x, y
2240 NEXT x
2250 FOR x = a - a / 50 TO -a STEP -a / 50
2260 y = -b * SQR(1 - x * x / (a * a))
2280 PRINT #2, x, y
2290 NEXT x

2300 NEXT k
2400 CLOSE #2
PRINT "The aspect ratio on the graphical display will show a circle as an"
PRINT "ellipse. Of the several orbits drawn, the outer one is the 'Circular'"
PRINT "orbit."

CALL Pager
PLAY "GEC"
       
        CHAIN "Tek2WPLT.BAS"

2500 END

        SUB Askn (n)
480 PRINT
490 PRINT "Please select largest value of the principal quantum"
500 PRINT "number";
510 INPUT n
520 IF n <> INT(n) THEN GOTO 490
530 IF n < 1 THEN GOTO 490
540 IF n > 10 THEN GOTO 560
550 GOTO 580
560 PRINT "Please try a smaller n for good graphical display."
570 GOTO 490
580 PRINT "k has the values of k=";
590 FOR I = 1 TO n
600 PRINT I; " ";
610 NEXT I
620 PRINT

END SUB

        SUB Pager
440 REM-----                                                     
450 PRINT , "Push return to continue";
460 INPUT t$
465 PRINT CHR$(12);
END SUB

        SUB Pict1
15
20 PRINT "This program calculates the electron orbits using"
30 PRINT "the sommerfeld orbits for the hydrogen atom."
40 PRINT "The orbits are a function of two quantum numbers,"
50 PRINT "n = the principal quantum number  n=1,2,3,...."
60 PRINT "k = the azimuthal quantum number  k=1,2,3,...,n"
70 PRINT " for the 3rd excited state, n=4,"
80 PRINT " k has the values k=1,2,3,4. There are 4 permitted "
90 PRINT "orbits of which three are ellispes and one"
100 PRINT "is circular."
110 PRINT

END SUB

        SUB Pict2
120 PRINT "The output of this program is a file that is used by the"
130 PRINT "program WPLOT to plot the several"
140 PRINT "electron trajectories on your PC."
150 PRINT " The semimajor and semiminor axes, a and b, are"
160 PRINT "given by:"
170 PRINT
180 PRINT , "a =     h^2 * n^2"
190 PRINT , "   ---------------"
200 PRINT , "     4 * pi^2 * u *e ^2 *z"
210 PRINT
220 PRINT "and"
230 PRINT , "b =       h^2 * n * k"
240 PRINT , "    ---------------------"
250 PRINT , "     4 * pi^ * e^2 *u * z"
260 PRINT

END SUB

        SUB Pict3
280 PRINT "where:"
290 PRINT , "h = planck's constant"
300 PRINT , "pi= 3.141592....."
310 PRINT , "u = the reduced mass"
320 PRINT , "z = the proton number....atomic number."
330 PRINT , "e = the electronic charge."

END SUB