C #TBMOS1 V1A 15-FEB-72. C LAST UPDATE: C FUNCTION TBMOS1(N1,N2,NR,NC) C C *PURPOSE. C TO CALCULATE THE 1-DIMENSIONAL MOSHINSKY TRANSFORMATION C BRACKET BETWEEN HARMONIC OSCILLATOR STATES IN LAB-CO-ORDINATES C AND RELATIVE-COM CO-ORDINATES. C C *PARAMETERS: C C N1 - INTEGER QUANTUM NUMBER OF FIRST PARTICLE STATE. C N2 - INTEGER QUANTUM NUMBER OF SECOND PARTICLE STATE. C NR - INTEGER QUANTUM NUMBER OF RELATIVE STATE. C NC - INTEGER QUANTUM NUMBER OF CENTRE-OF-MASS STATE. C C NOTE!! BY CONVENTION THE "N" QU-NRS ARE IN THE CLASS OF RADIAL C QUANTUM NUMBERS AND SO ARE DEFINED SO THAT "N"=0 IS THE C LOWEST STATE. C C INPUT PARAMETERS: C N1, N2, NR, NC C OUTPUT PARAMETERS: C (REAL FUNCTION VALUE ONLY) C C *METHOD. C A SINGLE SUMMATION FORMULA INVOLVING FACTORIALS HAS BEEN C DERIVED BY D.M.BRINK. SEE NOTES TO "TBMOS3" FOR REFERENCES. C THE SUM IS EVALUATED BY DOING THE FIRST TERM EXPLICITLY C AND USING A SIMPLE RECURRENCE FOR SUCCESSIVE TERMS. C C *ACCURACY. C THIS HAS NOT BEEN TESTED IN DETAIL BUT IT IS BELIEVED C THAT THE MACHINE SIGNIFICANCE IS THE LIMITING FACTOR AT C LEAST FOR SMALL QUANTUM NUMBERS . C C *RESTRICTIONS. C THERES IS NO CHECK TO MAKE SURE THAT THE QUANTUM NUMBERS C MAKE PHYSICAL SENSE. C C *ERROR CONDITIONS. C C *NON STANDARD ROUTINES CALLED. C FCTOR - FACTORIAL OF AN INTEGER ARGUMENT - MRMLIB. C PARITY- + OR -1 AS ARGUMENT EVEN OR ODD - MRMLIB. C C *TYPICAL TIMES. C C *ORIGIN. C SEE NOTE TO "TBMOS3". THIS VERSION BY M.R.MANNING. C C *COMMENTS. C C #END. C TBMOS1=0. MT=NR+NC IF(MT-N1-N2) 100,10,100 10 A=FCTOR(N2)*FCTOR(NR)/(FCTOR(N1)*FCTOR(NC) ) MD=NR-N1 NS=MD M=NR M2=N2 IF(MD) 20,30,30 20 MD=-MD NS=0 M=N1 M2=NC A=1./A 30 A=SQRT(A/FLOAT(2**MT) )*PARITY(NS)/FCTOR(MD) I=MD 35 TBMOS1=TBMOS1 + A T=(M2-I)*(M-I) IF(T) 100,100,40 40 I=I+1 S=(I-MD)*I A=-T*A/S GO TO 35 C 100 RETURN END