American Journal of Physics

Path integral solution to the infinite square well

Mark Goodman

Published Sep 1, 1981• 35 citations

Abstract

The infinite square-well potential in one dimension is solved using Feynman path integration. This solution uses an image point method equivalent to a sum over classical paths.

DOI: 10.1119/1.12720

Related papers

Solution of a particle's motion in a one-dimensional infinite square potential well using path integral

Chen Hao

A method to calculate the propagator for a particle moring in a one-dimensional infinite square well using Feynman's path integral is presented.Wave function and energy spectrum are derived from the propaga- tor,which manifest the equivalence between path integral and traditional methods.Meanwhile,a interesting mathematical function,Jacobi theta functionθ_3,is introduced.

College PhysicsJan 1, 20070 citations

Exact solution of the Feynman-Kac path integral for a point potential in an infinite square well

James M. Rejcek, Nail G. Fazleev, John L. Fry

APSOct 1, 20040 citations

Solution of a Particle's Motion in a Three-Dimensional Infinite Square Potential Well Using Path Integral

Wei Ji-jue

A path integral method to calculate the propagator for a particle moving in a three-dimensional infinite square well is presented and then its wave function and energy eigenvalue are derived.

Journal of Southwest UniversityJan 1, 20090 citations

Path integral solution to a charged particle in an infinite square-well potential with a constant electric field

Kyu Hwang Yeon, Chung‐In Um, Thomas F. George +1 more

The propagator of a charged particle in an infinite square-well potential in one dimension with a constant electric field is solved exactly using Feynman path integration. The wave function of the system is evaluated by the propagator. This wave function depends on time in a way determined by the well size, particle mass and charge, and applied electric field. The uncertainty relation of the system is also obtained by this function.

Canadian Journal of PhysicsSep 1, 19942 citations

Path-integral solution of a particle's motion in a two-dimensional infinite square potential well

Yuan Tong-quan

The path integral technique is used to calculate the propagator of a particle moving in a two-dimensional infinite square well.Its wave function and energy eigenvalue are obtained.

College PhysicsJan 1, 20090 citations

อนทกรลตามเสนทางสำหรบกำแพงศกยอนนต

อัฏฐชัย ถาวรสุวรรณ, วิทยา ทิพย์อักษร, นิคม ชูศิริ

บทความนี้ศึกษาปัญหากำแพงศักย์อนันต์ในหนึ่งมิติโดยอาศัยวิธีอินทิกรัลตามเส้นทางของฟายน์แมน ได้คำนวณ ตัวแผ่กระจายสำหรับกำแพงศักย์อนันต์โดยวิธีอินทิกรัลตามเส้นทางแบบลากรางเกียน ผลเฉลยที่ได้อาศัยวิธีจุดภาพ กระจกเงาซึ่งสมมูลกับการรวมเส้นทางแบบฉบับ ตัวแผ่กระจายที่ได้อยู่ในรูปแบบที่กระชับ และจากตัวแผ่กระจายดังกล่าว สามารถนำไปคำนวณหาสถานะเจาะจงโมเมนตัมและระดับพลังงานที่เป็นไปได้ของอนุภาคที่อยู่ภายใต้อิทธิพลของกำแพง ศักย์อนันต์ได้ In this paper we study an infinite potential barrier problem in one dimension using Feynman path integral approach. The propagator for the infinite potential barrier is calculated by means of the Lagrangian path integral. This solution uses an image-point method equivalent to a sum over classical paths. The propagator is evaluated in a closed form, and from this propagator we obtained the momentum eigenstates and possible energy levels of a particle under the influence of an infinite potential barrier.

ASEAN Journal of Scientific and Technological ReportsSep 21, 20160 citations