Back to Blog
Helium bohr model6/22/2023 ![]() ![]() Schrödinger equation for the two-electron Hamiltonian of helium. Have been computed quantum mechanically by numerically solving the Spectral properties and quantum-mechanical conceptsīy now considerable parts of the rich energy spectrum of the helium atom Which has proven very successful to this day. Which was subsequently replaced by the "new quantum theory": quantum (wave) mechanics The problems and failure of (most of) the attempts to quantize theĮlectron pair motion in helium marked the end of the "old quantum theory" For a comprehensive account of the developments of the semiclassical theory for helium up to the year 2000, see Tanner et al. Indeed, for chaotic systems such as the three-body problem helium, it is the entirety of all periodic orbits which conspire to form the energy levels such as beautifully shown in Gutzwiller's trace formula. The association of energy levels with individual periodic orbits in the old The Heisenberg model came closest to an adequate semiclassical description Though the good agreement must be considered as accidental, ![]() Not accept such half-integer orbital quantum numbers, Heisenberg never published his In his letter, Heisenberg arrived at a helium ionization potential of 24.6 V very close Of this configuration posted in a letter to Sommerfeld in 1922 is shown. Sides of the helium nucleus in Figure 3 Heisenberg's sketch Heisenberg, then a student of Sommerfeld, devised a different trajectoryĬonfiguration with the electrons moving on perturbed Kepler ellipses on different Kepler electron motion with quantized radii, respectively momenta p,įigure 3: Heisenberg's proposal for Kepler-type electron pair motion in helium (from Tanner et al. The energy levels of hydrogen by requiring periodic (elliptic) Modern semiclassical theory of the helium atom has its roots in the earlyĭays of quantum theory: The observation that atomic spectra consist of discrete lines calledįor a then novel theoretical approach, a quantum theory for atoms.īohr's early attempts were formulated in terms of quantum postulates and successfully reproduced ![]() Hence, helium as a microscopic three-bodyĬoulomb system has much in common with its celestial analogue, the gravitational Particles, are predominantly characterized by chaotic dynamics andĬannot be calculated analytically. Orbits of the two interacting electrons, when considered as classical Seemingly simple form of the underlying quantum Hamiltonian. Gives rise to exceedingly complicated spectral features, despite the The interplay between the attractive Coulomb interaction between the nucleusĪnd the electrons and the Coulomb repulsion between the electrons Nucleus with charge Z=2 and two electrons, see Figure 1. Helium, as the prototype of a two-electron atom, is composed of the Quantum chaos theory and in particular theįigure 1: The helium atom composed of two electrons and a nucleus of charge Z=2 (from Tanner et al. Two-electron atoms represent a paradigmatic system for the successful application of concepts of In helium, the classical dynamics is givenīy the pair of interacting electrons moving in the field of the (heavy) nucleus. Trajectories of the underlying classical system. The semiclassical theory of the helium atom (or other two-electron atoms)įollows the idea of computing and understanding the quantum energy levels starting from Helium and its role for the development of quantum mechanics Helium: an atomic three-body problem 4.4 Semiclassics for many-body problems.4.3 Double ionisation of helium for strong laser fields and ultra-short pulses - probing correlated electron-electron dynamics.4.2 Highly doubly excited states - recent advances.4.1 Exploring the full phase space - approximate symmetries and global structures.4 Recent developments and open questions.3.4 Semiclassical periodic orbit quantisation.3.3 Collisions, regularisation and the triple collision.3.2 Symbolic dynamics in the eZe collinear space.3.1.1 Symmetries and invariant subspaces.3 The helium atom - a semiclassical approach.2 Spectral properties and quantum-mechanical concepts.1.2 The failure of the "old quantum theory".1.1 Helium: an atomic three-body problem.1 Helium and its role for the development of quantum mechanics. ![]()
0 Comments
Read More
Leave a Reply. |