à High-Precision Value for the Quartic Anharmonic Oscillator Ground State

نویسنده

  • Michael Trott
چکیده

As it is well known, only a very limited number of one-dimensional potentials allow for an exact solution of the Schrödinger equation. This means that for many model potentials we must resort to numerical solution methods. For judging their accuracy, reliability, and speed, it is important to have high-precision values of certain nonexactly solvable potentials. The most investigated of such potentials is the quartic anharmonic oscillator (see [1] to [19]), described by

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

Some Unrelated Topics of Interest

This paper offers a demonstration of the appearance and general document features of the LaTeX_Article style sheet. Although the topics in this paper were written specifically for Publicon, it is hoped they will nonetheless be regarded with interest by the physics community. © 2004 Wolfram Research, Inc. 1 High-precision Value for the Quartic Anharmonic Oscillator Ground State

متن کامل

Analytic expression for exact-ground-state energy based on an operator method for a class of anharmonic potentials

A general procedure based on shift operators is formulated to deal with anharmonic potentials. It is possible to extract the ground-state energy analytically using our method provided certain consistency relations are satisfied. Analytic expressions for the exact-ground-state energy have also been derived specifically for a large class of the one-dimensional oscillator with cubic-quartic anharm...

متن کامل

Variational and norm criteria in high-order perturbative- variational wavefunctions

The behaviour of high-order perturbative-variational wavefunctions, with one or more free parameters, is studied. A variational criterion, and a criterion based upon variation of the norm of the perturbative approximation function with order, are used for fixing free parameters. For the quartic anharmonic oscillator, both criteria seem to be equivalent. The obtained energies, not only for groun...

متن کامل

A new approach to the logarithmic perturbation theory for the spherical anharmonic oscillator

The explicit semiclassical treatment of the logarithmic perturbation theory for the bound-state problem for the spherical anharmonic oscillator is developed. Based upon the h̄-expansions and suitable quantization conditions a new procedure for deriving perturbation expansions is offered. Avoiding disadvantages of the standard approach, new handy recursion formulae with the same simple form both ...

متن کامل

Quartic Anharmonic Oscillator And Random Matrix Theory

In this paper the relationship between the problem of constructing the ground state energy for the quantum quartic oscillator and the problem of computing mean eigenvalue of large positively de nite random hermitean matrices is established. This relationship enables one to present several more or less closed expressions for the oscillator energy. One of such expressions is given in the form of ...

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 2008