Imaginary cubic oscillator and its square-well approximation in p−representation

نویسنده

  • Miloslav Znojil
چکیده

Schrödinger equation with the imaginary, PT symmetric potential V (x) = i x is studied and discussed in momentum representation, via a solvable square-well approximation of its kinetic term.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Padé summability of the cubic oscillator

We prove the Padé (Stieltjes) summability of the perturbation series of the energy levels of the cubic anharmonic oscillator, H1(β) = p +x+ i p βx, as suggested by the numerical studies of Bender and Weniger. At the same time, we give a simple and independent proof of the positivity of the eigenvalues of the PT -symmetric operator H1(β) for real β (Bessis-Zinn Justin conjecture). All the n 2 N ...

متن کامل

Constrained Interpolation via Cubic Hermite Splines

Introduction In industrial designing and manufacturing, it is often required to generate a smooth function approximating a given set of data which preserves certain shape properties of the data such as positivity, monotonicity, or convexity, that is, a smooth shape preserving approximation.  It is assumed here that the data is sufficiently accurate to warrant interpolation, rather than least ...

متن کامل

Maximal Regularity of the Discrete Harmonic Oscillator Equation

We provide a geometrical interpretation for the best approximation of the discrete harmonic oscillator equation formulated in a general Banach space setting. We give a representation of the solution, and a characterization of maximal regularity-or well posednesssolely in terms of R-boundedness properties of the resolvent operator involved in the equation.

متن کامل

Applying reproducing kernels to the evaluation and approximation of the simple and time-dependent imaginary time harmonic oscillator path integrals

Reproduction of kernel Hilbert spaces offers an attractive setting for imaginary time path integrals, since they allow to naturally define a probability on the space of paths, which is equal to the probability associated with the paths in Feynman’s path integral formulation. This study shows that if the propagator is Gaussian, its variance equals the squared norm of a linear functional on the s...

متن کامل

Asymptotic solvability of an imaginary cubic oscillator with spikes

For complex potentials V (x) = −(ix)3 − β(ix) − 2 β δ (ix) which are PT symmetric we show that in the β ≫ 1 strong coupling regime the low lying bound states almost coincide with harmonic oscillators whenever the spectrum remains real (this means, at all δ < δcritical(β) ≈ 1). PACS 03.65.Fd 03.65.Ca 03.65.Ge 03.65.Bz

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2001