1 Introduction - Caltech High Energy Physics
... • Correlating with the increase in nodes, the higher the excited state, the greater the spatial frequency of the wave function oscillations. This corresponds to higher momenta, as expected from the deBroglie relation. • Each wave function has a region around y = 0 of oscillatory behavior, in which t ...
... • Correlating with the increase in nodes, the higher the excited state, the greater the spatial frequency of the wave function oscillations. This corresponds to higher momenta, as expected from the deBroglie relation. • Each wave function has a region around y = 0 of oscillatory behavior, in which t ...
You are going to read the chapter at home.
... (ci and ci ☨ ) is the same as for bosonic operators (bi and bi ☨ ): ci = annihilation operator; annihilates a particle in the state Ei ; ci☨ = creation operator; creates a particle in the state Ei ; ci☨ ci = occupation number operator for the state Ei . ...
... (ci and ci ☨ ) is the same as for bosonic operators (bi and bi ☨ ): ci = annihilation operator; annihilates a particle in the state Ei ; ci☨ = creation operator; creates a particle in the state Ei ; ci☨ ci = occupation number operator for the state Ei . ...
Physics Adiabatic Theorems for Dense Point Spectra*
... Theorem 4.1. Suppose that H(s) obeys (ϊ),(n) of Sect. 2 and that (l)-(6) holds. Then P obeys the adiabatic theorem. Proof We need only verify the hypothesis of Theorem 2.1 (2.iii) is implied by (2), so we need only prove (2.iv). Thus we concentrate on the equation ...
... Theorem 4.1. Suppose that H(s) obeys (ϊ),(n) of Sect. 2 and that (l)-(6) holds. Then P obeys the adiabatic theorem. Proof We need only verify the hypothesis of Theorem 2.1 (2.iii) is implied by (2), so we need only prove (2.iv). Thus we concentrate on the equation ...
Lesson 5
... For an arbitrary observable Ô with eigenvectors Φ n (x) and real eigenvalues on, the eigenfunctions form an orthogonal set that can be normalized so that ...
... For an arbitrary observable Ô with eigenvectors Φ n (x) and real eigenvalues on, the eigenfunctions form an orthogonal set that can be normalized so that ...
Outline of section 4
... (e.g. the Heisenberg microscope) (2) Arising from the properties of Fourier transforms (narrow spatial wavepackets need a wide range of wavevectors in their Fourier transforms and vice versa) (3) As a fundamental consequence of the fact that x and p are not compatible quantities so their correspondi ...
... (e.g. the Heisenberg microscope) (2) Arising from the properties of Fourier transforms (narrow spatial wavepackets need a wide range of wavevectors in their Fourier transforms and vice versa) (3) As a fundamental consequence of the fact that x and p are not compatible quantities so their correspondi ...
THE HVZ THEOREM FOR N
... N -particles moving on dN -dimensional lattice (Zd )N and interacting via short-range pair potentials. We prove the analogue of the HVZ theorem using the diagrammatic method of Hunziker for the case when particles have arbitrary bounded dispersion functions having not necessarily compact support. Mo ...
... N -particles moving on dN -dimensional lattice (Zd )N and interacting via short-range pair potentials. We prove the analogue of the HVZ theorem using the diagrammatic method of Hunziker for the case when particles have arbitrary bounded dispersion functions having not necessarily compact support. Mo ...