This paper studies the Schrodinger operator with a homogeneous electric field of the form -△+x<sub>1</sub>+V（x）, where x= （x<sub>1</sub>,…, x<sub>n</sub>）∈R<sup>n</s...This paper studies the Schrodinger operator with a homogeneous electric field of the form -△+x<sub>1</sub>+V（x）, where x= （x<sub>1</sub>,…, x<sub>n</sub>）∈R<sup>n</sup>. It is proved that in the specctral representation of the free Stark Hamiltonian, the time-delay operator in scattering theory can be expressed in trems of scattering matrix and under reasonable assumptions on the decay of the potential V, the on-shell time-delay operator is of trace class and its trace is related to the local spectral density via an explicit integral formula. Some asymptotics for the trace are estabhshed when the energy tends to infinity.展开更多
基金Partially supported by Ohinese NSF under grant No. 0187401by State Education Commission of China
文摘This paper studies the Schrodinger operator with a homogeneous electric field of the form -△+x<sub>1</sub>+V（x）, where x= （x<sub>1</sub>,…, x<sub>n</sub>）∈R<sup>n</sup>. It is proved that in the specctral representation of the free Stark Hamiltonian, the time-delay operator in scattering theory can be expressed in trems of scattering matrix and under reasonable assumptions on the decay of the potential V, the on-shell time-delay operator is of trace class and its trace is related to the local spectral density via an explicit integral formula. Some asymptotics for the trace are estabhshed when the energy tends to infinity.
