Time-Dependent Perturbation Theory

Z. Ficek

Published Apr 27, 2016• 0 citations

Abstract

Consider a two-level atom represented by the spin operators σ ^ ± , σ ^ Z , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429092053/5e12ab0e-ba42-4caa-9bdf-6325e9117d3e/content/ineqn19_1.tif"/> interacting with a one-dimensional harmonic oscillator, represented by the creation and annihilation operators â † and â . The Hamiltonian of the system is given by ( 19.1 ) H ^ = 1 2 ℏ ω 0 σ ^ Z + ℏ w 0 ( a ^ † a ^ + 1 2 )− 1 2 i ℏ g + ( σ ^ + a ^ − σ ^ − a ^ † ) . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429092053/5e12ab0e-ba42-4caa-9bdf-6325e9117d3e/content/eqn19_1.tif"/>

DOI: 10.1201/b20046-18

Related papers

Time-Independent Perturbation Theory

Z. Ficek

In an orthonormal basis, a linear operator Â is represented by the matrix ( 18.1 ) A ˆ = ( 2 λ 1+ λ 1+ λ λ ) , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429092053/5e12ab0e-ba42-4caa-9bdf-6325e9117d3e/content/eqn18_1.tif"/>

Apr 27, 20160 citations

Time—Dependent Perturbation Theory

Şaki̇r Erkoç

Systems described by a time–independent potential energy function, V ( r , t ) = V ( r ), are the subject of quantum statics . Such systems may be studied by the time–dependent Schrödinger equation 16.1 H Ψ = i ℏ ∂ Ψ ∂ t https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429136528/397e01c1-e101-4a47-b552-a910642bbb8c/content/eqn16_1.tif"/>

CRC Press eBooksJul 28, 20060 citations

Schrödinger Equation

Lukong Cornelius Fai

In the previous chapter, we did not examine the change of a state with time https://www.w3.org/1998/Math/MathML"> t https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003273073/d236e21f-f9f6-4e42-b186-ef1c50f0a68b/content/math2_1.tif" xmlns:xlink=" https://www.w3.org/1999/xlink "/> . It has been assumed that we have been examining a state at a given moment https://www.w3.org/1998/Math/MathML"> t https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003273073/d236e21f-f9f6-4e42-b186-ef1c50f0a68b/content/math2_2.tif" xmlns:xlink=" https://www.w3.org/1999/xlink "/> . In the general case, the state of a system changes with time https://www.w3.org/1998/Math/MathML"> t https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003273073/d236e21f-f9f6-4e42-b186-ef1c50f0a68b/content/math2_3.tif" xmlns:xlink=" https://www.w3.org/1999/xlink "/> . For example, say the motion of an electron in a potential field, its wave function depends on time https://www.w3.org/1998/Math/MathML"> t https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003273073/d236e21f-f9f6-4e42-b186-ef1c50f0a68b/content/math2_4.tif" xmlns:xlink=" https://www.w3.org/1999/xlink "/> : https://www.w3.org/1998/Math/MathML"> Ψ = Ψ q , t https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003273073/d236e21f-f9f6-4e42-b186-ef1c50f0a68b/content/math2_5.tif" xmlns:xlink=" https://www.w3.org/1999/xlink "/> . Such a dependence has to be described by a differential equation in which we may have https://www.w3.org/1998/Math/MathML"> ∂ Ψ ∂ t , ∂ 2 Ψ ∂ t 2 , ⋯ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003273073/d236e21f-f9f6-4e42-b186-ef1c50f0a68b/content/math2_6.tif" xmlns:xlink=" https://www.w3.org/1999/xlink "/> .

CRC Press eBooksApr 19, 20220 citations

Quantum Dynamics and Pictures

Z. Ficek

Consider a two-level atom of energy states |1〉 and |2〉 driven by a laser field. The atom can be represented as a spin − 1 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429092053/5e12ab0e-ba42-4caa-9bdf-6325e9117d3e/content/ineqn14_1.tif"/> particle and the laser field can be treated as a classical field. The Hamiltonian of the system is given by ( 14.1 ) H ^ = 1 2 ℏ ω 0 σ ^ Z − 1 2 i ℏ Ω ( σ ^ + e − i ω L t − σ ^ − e i ω L t ), https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429092053/5e12ab0e-ba42-4caa-9bdf-6325e9117d3e/content/eqn14_1.tif"/>

Apr 27, 20160 citations

Time-Dependent Interaction Between a Two-Level Atom and N Two-Level Atoms in Terms of su(2) Lie Algebra

M. Sebawe Abdalla, Eied Mahmoud Khalil, A.‐S. F. Obada

Journal of Russian Laser ResearchJan 1, 20172 citations

Exact Wave Function of a Time-Dependent Harmonic Oscillator

Tae Jun Park

Increasing theoretical attention has been paid to solving exactly time-dependent quantum mechanical problems for their own mathematical interest and for applications.Among

Bulletin of the Korean Chemical SocietyFeb 20, 20023 citations