Notes on the Riccati Equation
2005 ◽
Vol 70
(7)
◽
pp. 941-950
◽
Keyword(s):
The relationship between the Riccati and Schrödinger equations is discussed. It is shown that the transformation converting the Riccati equation into its normal form is expressed in terms of the roots of its algebraic part treated as a second-order polynomial. Together with the well-known Riccati transformation, a new transformation which also links the Riccati equation to the second-order linear differential equation is introduced. The latter is actually the Riccati transformation applied to an "inverse" Riccati equation. Two specific forms of the Riccati equation admitting the explicit particular rational solutions are obtained.
1993 ◽
Vol 118
(3)
◽
pp. 813-813
◽
1986 ◽
Vol 102
(3-4)
◽
pp. 253-257
◽
2018 ◽
Vol 973
◽
pp. 012057
◽
1965 ◽
Vol 14
(3)
◽
pp. 327-334
◽
1987 ◽
Vol 123
(2)
◽
pp. 366-375
1963 ◽
Vol 27
(3)
◽
pp. 847-861
2014 ◽
Vol 57
◽
pp. 44-59
◽
1949 ◽
Vol 35
(4)
◽
pp. 190-191
◽