TY - JOUR
T1 - An implicit spectral formula for generalized linear schrödinger equations
AU - Schulze-Halberg, Axel
AU - GarcÍa-Ravelo, Jesús
AU - Gil, José Juan Peña
PY - 2009/10
Y1 - 2009/10
N2 - We generalize the semiclassical BohrSommerfeld quantization rule to an exact, implicit spectral formula for linear, generalized Schrödinger equations admitting a discrete spectrum. Special cases include the position-dependent mass Schrödinger equation or the Schrödinger equation for weighted energy. Requiring knowledge of the potential and the solution associated with the lowest spectral value, our formula predicts the complete spectrum in its exact form.
AB - We generalize the semiclassical BohrSommerfeld quantization rule to an exact, implicit spectral formula for linear, generalized Schrödinger equations admitting a discrete spectrum. Special cases include the position-dependent mass Schrödinger equation or the Schrödinger equation for weighted energy. Requiring knowledge of the potential and the solution associated with the lowest spectral value, our formula predicts the complete spectrum in its exact form.
KW - Bohr-Sommerfeld rule
KW - Discrete spectrum
KW - Generalized Schrodinger equation
UR - http://www.scopus.com/inward/record.url?scp=70450176208&partnerID=8YFLogxK
U2 - 10.1142/S0218301309013890
DO - 10.1142/S0218301309013890
M3 - Artículo
SN - 0218-3013
VL - 18
SP - 1831
EP - 1844
JO - International Journal of Modern Physics E
JF - International Journal of Modern Physics E
IS - 9
ER -