Solution of the Rovibrational Schrödinger Equation of a Molecule Using the Volterra Integral Equation
Table 1
The energy eigenvalues , the rotational constants , and the centrifugal distortion constants ,, of the pure vibrational energy levels of the Morse potential of CO molecule.
V
cm−1
cm−1
× 106 cm−1
× 1012 cm−1
× 1017 cm−1
0
1081.78
1.9225
6.11954
5.8008
3.6445
1081.61
0.02
1081.5857
0.02
1
3225.05
1.9050
6.11885
5.6556
3.7160
3225.05
0.00
3224.8568
0.03
2
5341.84
1.8875
6.11849
5.5100
3.7848
5342.11
0.00
5341.6478
0.00
3
7432.22
1.8700
6.11844
5.3659
3.8409
7432.79
0.01
7432.0247
0.00
4
9496.25
1.8525
6.11863
5.2272
3.8678
9497.09
0.18
9496.0550
0.00
5
11534.03
1.8350
6.11892
5.1007
3.8397
11535.01
0.01
11533.80787
0.00
6
13545.61
1.8175
6.11910
4.9970
3.7184
13546.56
0.00
13545.3543
0.00
7
15531.12
1.8001
6.11884
4.9323
3.4491
15531.72
0.00
15530.767
0.00
8
17490.66
1.7826
6.11761
4.9298
2.9556
17490.1202
0.00
9
19424.39
1.7652
6.11467
5.0224
2.2224
19423.4901
0.00
10
21332.48
1.7478
6.10895
5.2545
0.8581
21330.9539
0.01
11
23195.48
1.7353
6.3063
5.1176
7.4807
23212.5907
0.07
12
25046.37
1.7179
6.3265
4.8608
7.7559
25068.4807
0.09
13
26870.69
1.7004
6.3476
4.5905
8.0499
26898.7056
0.10
14
28668.43
1.6829
6.3695
4.3061
8.3641
28703.3478
0.00
15
30439.59
1.6653
6.3922
4.0066
8.7004
30482.4908
0.14
16
32184.18
1.6476
6.4159
3.6911
9.0606
32236.2189
0.16
17
33902.19
1.6299
6.4405
3.3586
9.4470
33964.6167
0.18
18
35593.63
1.6121
6.4661
3.0081
9.8617
35667.7691
0.21
19
37258.49
1.5943
6.4927
2.6384
10.307
37345.7608
0.23
20
38896.77
1.5764
6.5204
2.2483
10.787
38998.6766
0.26
21
40508.47
0.29
1.5584
6.5493
1.8363
11.303
40626.6001
22
42093.6
1.5403
6.5794
1.4011
11.859
42229.6144
0.32
23
43652.15
1.5221
6.6108
9.4096
12.460
43807.8009
0.36
24
45184.13
1.5039
6.6435
4.5424
13.109
45361.2396
0.39
25
46689.52
1.4856
6.6775
6.0978
13.812
46890.0081
0.43
26
48168.35
1.4672
6.7131
6.0676
14.573
48394.1814
0.47
27
49620.59
1.4488
6.7502
1.1853
15.398
49873.8318
0.51
28
51046.26
1.4302
6.7890
1.7992
16.295
51329.0276
0.55
29
52445.35
1.4116
6.8295
2.4510
17.270
52759.8334
0.60
30
53817.87
1.3929
6.8718
3.1438
18.332
54166.3090
0.65
31
55163.8
1.3741
6.9160
3.8807
19.496
55548.5091
0.70
32
56483.17
1.3552
6.9623
4.6654
20.757
56906.4825
0.75
33
57775.95
1.3362
7.0107
5.5017
22.142
58240.2716
1.11
34
59042.17
1.3171
7.0614
6.3942
23.660
59711.7
1.12
35
60281.79
1.2979
7.1145
7.3475
25.327
60835.4299
0.92
36
61494.85
1.2785
7.1702
8.3670
27.299
62096.8449
0.98
37
62681.33
1.2591
7.2286
9.4589
29.181
63334.1657
1.04
38
63841.23
1.2396
7.2899
10.630
31.412
63547.399
0.46
39
64974.55
1.2200
7.3543
11.887
33.881
65736.5076
1.17
40
66081.3
1.2002
7.4220
13.238
36.619
66901.4905
1.24
The first entry is for the present work. The second and the third entries are, respectively, for [14, 15].
