scholarly journals INVARIANT-RELATED UNITARY TRANSFORMATION METHOD AND EXACT SOLUTIONS FOR THE QUANTUM DIRAC FIELD IN A TIME-DEPENDENT SPATIALLY HOMOGENEOUS ELECTRIC FIELD

1999 ◽  
Vol 48 (6) ◽  
pp. 1011
Author(s):  
FU JIAN ◽  
GAO XIAO-CHUN ◽  
XU JING-BO ◽  
ZOU XU-BO
Keyword(s):  
Electric Field ◽  
Exact Solutions ◽  
Unitary Transformation ◽  
Transformation Method ◽  
Time Dependent ◽  
Dirac Field ◽  
Homogeneous Electric Field ◽  
Spatially Homogeneous

EXACT SOLUTIONS OF SCHRODINGER’S EQUATION FOR SPIN SYSTEMS IN A CLASS OF TIME-DEPENDENT MAGNETIC FIELDS

1991 ◽  
Vol 05 (29) ◽  
pp. 1919-1924 ◽  
Author(s):  
M.J. TAHMASEBI ◽  
Y. SOBOUTI
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Exact Solutions ◽  
Spin System ◽  
Schrodinger Equation ◽  
Unitary Transformation ◽  
Variable Magnetic Field ◽  
Spin Systems ◽  
Time Variable ◽  
Time Dependent

A spin system in a time variable magnetic field is considered. For certain fields there exists a frame in which the Hamiltonian becomes static. The criterion for such fields is derived. The unitary transformation that accomplishes this task is obtained and the underlying Schrodinger equation is solved exactly.

scholarly journals Time-Dependent Unitary Transformation Method in the Strong-Field-Ionization Regime with the Kramers-Henneberger Picture

2021 ◽  
Vol 22 (16) ◽  
pp. 8514
Author(s):  
Je-Hoi Mun ◽  
Hirofumi Sakai ◽  
Dong-Eon Kim
Keyword(s):  
Unitary Transformation ◽  
Strong Field ◽  
Three Dimensional ◽  
Transformation Method ◽  
Time Dependent ◽  
Moving Frame ◽  
Evolution Operators ◽  
Step Size ◽  
One Dimensional ◽  
Strong Field Ionization

Time evolution operators of a strongly ionizing medium are calculated by a time-dependent unitary transformation (TDUT) method. The TDUT method has been employed in a quantum mechanical system composed of discrete states. This method is especially helpful for solving molecular rotational dynamics in quasi-adiabatic regimes because the strict unitary nature of the propagation operator allows us to set the temporal step size to large; a tight limitation on the temporal step size (δt<<1) can be circumvented by the strict unitary nature. On the other hand, in a strongly ionizing system where the Hamiltonian is not Hermitian, the same approach cannot be directly applied because it is demanding to define a set of field-dressed eigenstates. In this study, the TDUT method was applied to the ionizing regime using the Kramers-Henneberger frame, in which the strong-field-dressed discrete eigenstates are given by the field-free discrete eigenstates in a moving frame. Although the present work verifies the method for a one-dimensional atom as a prototype, the method can be applied to three-dimensional atoms, and molecules exposed to strong laser fields.

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