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Aalborg Universitet
Aalborg Universitet

Infinite Square Well.wxp
Infinite Square Well.wxp

... Schrodinger's Equation and the Infinite Square Well The Wave Function and Probability We have examined some of the arguments that lead scientists in the first years of the 1900's to conclude that light was actually composed of individual elements called “photons”, each with its own unique energy (I ...
Modified Schrödinger equation, its analysis and experimental
Modified Schrödinger equation, its analysis and experimental

... vP → ∞ there is tP = 0, ϑ = t, and modified equations (7) and (8) become identical to classical equations (1) and (2), respectively. Solutions of classical time dependent Schrödinger parabolic type equation (1) predict that any local perturbation introduced at initial moment of time t0 = 0, instan ...
2Cpolyachenko.pdf
2Cpolyachenko.pdf

... reduced to a simple integral equation in the form of the classical eigen-value problem. Here we demonstrate that this integral equation can be obtained as a special case of a general eigen-value problem, applicable to the study of small perturbations in any integrable system, i.e. its potential admi ...
On the Physical Origin of the Lamb Shift
On the Physical Origin of the Lamb Shift

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A Spin Chain Primer - University of Miami Physics
A Spin Chain Primer - University of Miami Physics

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Physics Adiabatic Theorems for Dense Point Spectra*
Physics Adiabatic Theorems for Dense Point Spectra*

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The Schrödinger equation Combining the classical Hamilton

Quantum Mechanical Path Integrals with Wiener Measures for all
Quantum Mechanical Path Integrals with Wiener Measures for all

... e = T/(N+1), and (8= (1 —ev/2)/(1+ ev/2), v fixed and positive (v is the diffusion constant, as will become apparent). With these identifications, and for polynomially bounded h, we are able to prove5 s ("s" ...
Quantum Physics II, Lecture Notes 6
Quantum Physics II, Lecture Notes 6

... The state space of quantum mechanics –the Hilbert space H of states – is best thought as a space with time-independent basis vectors. There is no role for time in the definition of the state space H. In the Schrödinger “picture” of the dynamics, the state that represents a quantum system depends on ...
Quantum Mechanics of Lowest Landau Level Derived from N= 4
Quantum Mechanics of Lowest Landau Level Derived from N= 4

Quantum typicality: what is it and what can be done... Jochen Gemmer LMU Muenchen, May, Friday 13th, 2014 University of Osnabrück,
Quantum typicality: what is it and what can be done... Jochen Gemmer LMU Muenchen, May, Friday 13th, 2014 University of Osnabrück,

Full Current Statistics in the Regime of Weak Coulomb Interaction
Full Current Statistics in the Regime of Weak Coulomb Interaction

... There are two important manifestations of the quantization of the electric charge. The first is a current shot noise [1]. In mesoscopic conductors with large conductance G  GQ , GQ  e2 =2h being the conductance quantum, the quantum mechanical Pauli principle modifies the shot noise with respect ...


Quantum Chemistry - Eric R. Bittner
Quantum Chemistry - Eric R. Bittner

... chemistry courses will focus upon electronic structure. In fact, the moniker “quantum chemistry” typically refers to electronic structure theory. While this is an extremely rich topic, it is my personal opinion that a deeper understanding of dynamical processes provides a broader basis for understan ...
Resonance hit
Resonance hit

Morse potential derived from first principles
Morse potential derived from first principles

... The quantum harmonic oscillator (QHO) is certainly one of the most celebrated paradigms in quantum mechanics. Among its several important attributes, the QHO can be solved exactly and has been consistently used to approximate any potential function when Taylor expanded around their minima till secon ...
Generalized quantum mechanical two-Coulomb
Generalized quantum mechanical two-Coulomb

PDF document
PDF document

... with the appropriate equation of state. In order to calculate the fluid-solid part of the phase diagram it is often necessary to apply two different theories: one to describe the fluid phase, and another to characterize the equilibrium solid. In this contribution we will explore two theoretical appr ...
Lecture Notes: Condensed Matter Theory I (TKM1)
Lecture Notes: Condensed Matter Theory I (TKM1)

The Toda Lattice
The Toda Lattice

Simple, accurate electrostatics-based formulas for calculating
Simple, accurate electrostatics-based formulas for calculating

TWO-STATE SYSTEMS
TWO-STATE SYSTEMS

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Perturbation theory (quantum mechanics)

In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for which a mathematical solution is known, and add an additional ""perturbing"" Hamiltonian representing a weak disturbance to the system. If the disturbance is not too large, the various physical quantities associated with the perturbed system (e.g. its energy levels and eigenstates) can be expressed as ""corrections"" to those of the simple system. These corrections, being small compared to the size of the quantities themselves, can be calculated using approximate methods such as asymptotic series. The complicated system can therefore be studied based on knowledge of the simpler one.
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