TY - JOUR
T1 - Time evolution of superoscillations for the Schrödinger equation on R\ { 0 }
AU - Schlosser, Peter
N1 - Publisher Copyright:
© 2022, The Author(s).
PY - 2022/8
Y1 - 2022/8
N2 - In quantum mechanics, superoscillations, or the more general supershifts, appear as initial conditions of the time-dependent Schrödinger equation. Already in [5], a unified approach was developed, which yields time persistence of the supershift property under certain holomorphicity and growth assumptions on the corresponding Green’s function. While that theory considers the Schrödinger equation on the whole real line R, this paper takes the natural next step and considers R\ { 0 } , while allowing boundary conditions at x= 0 ±. In particular, the singular 1x2-potential as well as the very important δ and δ′ distributional potentials are covered.
AB - In quantum mechanics, superoscillations, or the more general supershifts, appear as initial conditions of the time-dependent Schrödinger equation. Already in [5], a unified approach was developed, which yields time persistence of the supershift property under certain holomorphicity and growth assumptions on the corresponding Green’s function. While that theory considers the Schrödinger equation on the whole real line R, this paper takes the natural next step and considers R\ { 0 } , while allowing boundary conditions at x= 0 ±. In particular, the singular 1x2-potential as well as the very important δ and δ′ distributional potentials are covered.
KW - Fresnel integral
KW - Green’s function
KW - Schrödinger equation
KW - Superoscillations
KW - Supershift
UR - http://www.scopus.com/inward/record.url?scp=85131956693&partnerID=8YFLogxK
U2 - 10.1007/s40509-022-00272-2
DO - 10.1007/s40509-022-00272-2
M3 - Article
AN - SCOPUS:85131956693
SN - 2196-5609
VL - 9
SP - 343
EP - 366
JO - Quantum Studies: Mathematics and Foundations
JF - Quantum Studies: Mathematics and Foundations
IS - 3
ER -