Blackbody quantum mechanics

Several questions present themselves immediately How good does the initial guess have to be How do we know that the procedure leads to better guesses, not worse How many steps (how long) will the procedure take How do we know when to stop These questions and others like them will play an important role in this book. You will not be surprised to leam that answers to questions like these vary from one problem to another and cannot be set down once and for all. Let us start with a famous problem in quantum mechanics blackbody radiation. 

In principle, emission spectroscopy can be applied to both atoms and molecules. Molecular infrared emission, or blackbody radiation played an important role in the early development of quantum mechanics and has been used for the analysis of hot gases generated by flames and rocket exhausts. Although the availability of FT-IR instrumentation extended the application of IR emission spectroscopy to a wider array of samples, its applications remain limited. For this reason IR emission is not considered further in this text. Molecular UV/Vis emission spectroscopy is of little importance since the thermal energies needed for excitation generally result in the sample s decomposition. 

Although historians of science have studied the breakthrough that led to quantum mechanics, nobody can be exactly sure what was in Planck s orderly, disciplined mind when he devised the equation that revolutionized physics. He tackled the blackbody problem in several ways, but nothing worked. Finally, he tried an idea that was contradictory to all established concepts at the time What if energy was not continuous What if blackbodies absorbed and emitted it in little chunks He wrote down his equation ... 

When Planck used this relationship to calculate the spectrum of blackbody radiation, he came up with a result that agreed perfectly with experiment. More importantly, he had discovered quantum mechanics. Energy emitted by a blackbody is not continuous. Instead, it comes in tiny, irreducible packets or quanta (a word coined by Planck himself) that are proportional to the frequency of the oscillator that generated the radiation. 

A blackbody is a body that absorbs all radiation and emits none. Experimentally, it is approximated by a "furry box" (a closed box of aluminum, whose interior walls are anodized to form a black surface, or a metal box painted with carbon black) and with a small hole drilled in one face, to allow some radiation generated at any fixed temperature to escape the box. The puzzle in the late nineteenth century was to explain the experimentally observed wavelength dependence and temperature dependence of the radiation (Fig. 5.5). Partial explanations had been obtained by Rayleigh21 and Jeans22 and by Stefan23 and Boltzmann, but the full, exact, correct, and truly revolutionary explanation was obtained in 1901 by Planck,24 who thereby ushered in quantum mechanics. 

We have introduced you to the concepts and methods of quantum mechanics this branch of physics was developed to explain the behavior of matter on the nanometer length scale. The results of a number of key experiments demanded the creation of a new physical theory classical mechanics and electrodynamics failed completely to account for these new observations. The pivotal experiments and observations included the spectrum and temperature dependence of blackbody radiation, the very existence of stable atoms and their discrete line spectra, the... 

Describe blackbody radiation, and discuss how related paradoxes of classical physics were resolved by quantum mechanics (Section 4.2, Problems 9 and 10). 

Quantum mechanics represents one of the cornerstones of modem physics. Though there were a variety of different clues (such as the ultraviolet catastrophe associated with blackbody radiation, the low-temperature specific heats of solids, the photoelectric effect and the existence of discrete spectral lines) which each pointed towards quantum mechanics in its own way, we will focus on one of these threads, the so-called wave-particle duality, since this duality can at least point us in the direction of the Schrodinger equation. 

More than a century has passed since Planck discovered that it is possible to explain properties of the blackbody radiation by introducing discrete packets of energy, which we now call photons. The idea of discrete or quantized nature of energy had deep consequences and resulted in development of quantum mechanics. The quantum theory of optical fields is called quantum optics. The construction of lasers in the 1960s gave impulse to rapid development of nonlinear optics with a broad variety of nonlinear optical phenomena that have been... 

The study of the blackbody radiation, which lead to the formulation of quantum mechanics by Max Plank. 

Planck (1901) was the first to discard classical mechanics to explain blackbody radiation when he proposed that an oscillator could only acquire and lose energy in discrete units, called quanta. The magnitude of the quantum of energy was not fixed, but depended on the change in the oscillator energy E according to the equation... 

---