The Hartree-Fock Method for Approximating Wave Functions in Quantum Chemistry
The Hartree-Fock Method
For hydrogen, the exact wave function is known. For lithium and helium, very accurate wave functions have been calculated by including interelectronic distance in the variation function. For atoms of higher atomic number, the best approach to finding a good wave function lies in first calculating an approximate wave function using the Hartree-Fock procedure, which we shall outline in this section. The Hartree-Fock method is the basis for the use of atomic and molecular orbitals
Read MoreUnderstanding the Ellipse: Equations, Characteristics, and Examples
Ellipse as a Geometric Locus
The ellipse is defined as the geometrical locus formed by the set of all points in the plane, where the sum of the distances from two fixed points, known as the foci (plural of focus) of the ellipse, is a constant.
Characteristics and Elements of the Ellipse
V and V’ are the vertices of the ellipse and are also known as the endpoints of the major axis.
F and F’ are the foci of the ellipse.
B and B’ are the endpoints of the minor axis.
Segment 
is known as the major axis
Understanding Hyperbolas: Equations, Characteristics, and Examples
Hyperbola as a Geometric Locus
The hyperbola is defined as the geometric locus of all points in a plane where the difference of distances from two fixed points (called foci) is constant.
The equation of a hyperbola is similar to that of an ellipse, but instead of the sum of distances, it involves the difference of distances.
Ordinary Form of the Hyperbola Equation
Hyperbola with Horizontal Focal Axis and Center at the Origin (0, 0)
The equation for this hyperbola is: x2/a2 – y2/b2 = 1
Characteristics:
Read MoreThe Life and Works of Henry Wadsworth Longfellow
Henry Wadsworth Longfellow: A Life in Poetry
Early Life and Education
February 27, 1807: Henry Wadsworth Longfellow born
1813: Begins attending Portland Academy
1820: First published poem, “The Battle of Lovell’s Pond,” appears in the Portland Gazette
1821: Enrolled at Bowdoin College in Brunswick, ME. Stays in Portland for the first year of studies
1825: Graduates from Bowdoin College
Travels, Teaching, and Marriage
1826-1829: Travels and studies in Europe
1829-1835: Teaches at Bowdoin College
1831: Marries
Read MorePhase Transformations and Material Properties in Metallurgy
An Equilibrium Reaction: Monotectic
A monotectic reaction is one in which a molten solution, upon cooling, becomes immiscible. This process can lead to material defects like cracking.
Portevin Rules
- In each balancing zone, only two phases can exist at most.
- Except for the liquid phase region, all other single-phase regions are occupied by solid phases.
- When crossing a line in the phase diagram, the number of phases varies by one.
- Any region bounded by a horizontal line contains two phases.
- Two-phase regions
Stellar Spectroscopy and Evolution: A Comprehensive Guide
Chapter 8: Spectroscopy of Stars
- What does ‘luminosity’ mean?
Luminosity refers to the total energy radiated by a star per second. The larger a star’s surface area, the greater its luminosity. - What is the equation relating apparent brightness to luminosity? Which tells us more about a star: its luminosity or its brightness?
The equation is L = b/d², where L is luminosity, b is apparent brightness, and d is distance. Luminosity tells us more about a star’s intrinsic properties. To determine a star’s