## Shockley—Queisser Efficiency Limit

With a load of matched impedance, the output power of a solar cell can be maximized. As shown in Section 9.1.3, the maximum power is related to the nominal power by a form factor nf approximately

## Statistics of Particles

In the microscopic treatment of matter, the particles, for example, molecules and elec­trons, are distributed in a system of energy levels. How the particles distribute among the energy levels determines the behavior of the system in a significant way. Regarding to applications with solar energy, an understanding of Maxwell-Boltzmann statistics and Fermi-Dirac statistics is essential. […]

## 1 Harmonic Oscillator

The Hamiltonian of a one-dimensional harmonic oscillator is – 1 a2 mj2 ff = 2mp + ~q • where the momentum p and coordinate q satisfy the commutation relation [p, q] = pq — qp = ih. We introduce a pair of operators, the annihilation operator, Physics of Solar Energy C. Julian Chen Copyright © […]

## Quantum Mechanics Primer

Usually, introductory quantum mechanics starts with Schrodinger’s equation and using partial differential equations as the mathematical tools. For example, the hydrogen atom problem is resolved with spherical harmonics and Laguerre polynomials. A possi­ble shortcoming with this approach is that the readers become submerged in pages and pages of mathematical formulas and lose the conceptual understanding […]

## Sine Formula

In planar trigonometry, there is the sine formula abcsin A sin B sin C In spherical trigonometry, a similar formula exists, sin a sin b sin c sin A sin B sin C Obviously, for small arcs, Eq. B.15 reduces to Eq. B.14. To prove Eq. B.15, we rewrite Eq. B.2 as sin b sin […]

## Cosine Formula

In planar trigonometry, there is a cosine formula a2 = b2 + c2 – 2bc cos A. (B.1) In spherical trigonometry, a similar formula exists: cos a = cos b cos c + sin b sin c cos A. (B.2) When the arcs are short and the spherical triangle approaches a planar triangle, Eq. B.2 […]

## Spherical Triangle

A plane passing through the center of a sphere O cuts the surface in a circle, which is called a great circle. For any two points A and B on the sphere, if the line AB does not pass the center O, there is one and only one great circle which passes both points. The […]

## Spherical Trigonometry

When we look into the sky, it seems that the Sun and all the stars are located on a sphere of a large but unknown radius. In other words, the location of the Sun is defined by a point on the celestial sphere. On the other hand, the surface of Earth is, to a good […]