scholarly journals Lie theory and separation of variables. 7. The harmonic oscillator in elliptic coordinates and Ince polynomials

1975 ◽  
Vol 16 (3) ◽  
pp. 512-517 ◽  
Author(s):  
C. P. Boyer ◽  
E. G. Kalnins ◽  
W. Miller
Keyword(s):  
Harmonic Oscillator ◽  
Separation Of Variables ◽  
Lie Theory ◽  
Elliptic Coordinates

scholarly journals Lie theory and separation of variables. 4. The groups SO (2,1) and SO (3)

1974 ◽  
Vol 15 (8) ◽  
pp. 1263-1274 ◽  
Author(s):  
E. G. Kalnins ◽  
Willard Miller
Keyword(s):  
Separation Of Variables ◽  
Lie Theory

scholarly journals Applications of the Lie theory of extended groups in Hamiltonian mechanics: the oscillator and the Kepler problem

1981 ◽  
Vol 23 (2) ◽  
pp. 173-186 ◽  
Author(s):  
P. G. L. Leach
Keyword(s):  
Harmonic Oscillator ◽  
Kepler Problem ◽  
Three Dimensional ◽  
Equation Of Motion ◽  
Hamiltonian Mechanics ◽  
Lie Theory ◽  
Newtonian Equation ◽  
Constants Of Motion

AbstractThe method of the Lie theory of extended groups has recently been formulated for Hamiltonian mechanics in a manner which is consistent with the results obtained using the Newtonian equation of motion. Here the method is applied to the three-dimensional time-independent harmonic oscillator and to the classical Kepler problem. The expected constants of motion are obtained. Previously unobserved relations between generators and invariants are also noticed.

scholarly journals Lie theory and separation of variables. 3. The equation ftt−fss =γ2f

1974 ◽  
Vol 15 (7) ◽  
pp. 1025-1032 ◽  
Author(s):  
E. G. Kalnins ◽  
W. Miller
Keyword(s):  
Separation Of Variables ◽  
Lie Theory

Lie theory and separation of variables. 6. The equation iUt + Δ2U = 0

1975 ◽  
Vol 16 (3) ◽  
pp. 499-511 ◽  
Author(s):  
C. P. Boyer ◽  
E. G. Kalnins ◽  
W. Miller
Keyword(s):  
Separation Of Variables ◽  
Lie Theory
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