This course uses Excel heavily as a tool for demonstrating numerical manipulations. Excel is powerful and can do essentially everything that one would need. However, the poor quality of the graphics and difficulty of syntax make Excel are obstacles for many users. Several competing scientific software packages have been developed. The most common of these are Igor and Origin. They are both similar in their capabilties and the choice is really a matter of taste and convenience.
The emission spectra of stars give us information about the emission of all objects in the universe. Stars are convenient because they are very bright and we can measure the distribution of energy emitted at different wavelengths even using fairly simple devices. Therefore, scientists knew that different stars had different emission spectra and different maxima. The emission is known as "blackbody emission". This is a terrible name, at least for students since blackbodies are not black at all. The physicists surely knew what they meant by blackbody radiation, but let's just call it thermal radiation. The point is that star's have a thermal radiation spectrum that follows the Wien displacement law. In this course we have chosen to use Igor as an alternative to Excel. The segments in this section are devoted to demosntrations of a small number of the capabilities of Igor that are most likely to be relevant to this course.
Reading in data
Of course, with any such program the entry of data into the program is an important step. Both Igor and Excel provide two general methods.
1. Read the data in from a file using various formats to determine how many data columns are available to be read.
2. Copy and paste the data into a spreadsheet. Igor has a spreadsheet that is visible as soon as the program is opened.
Fitting data
Both linear regression and non-linear fitting are available in Igor. Unlike Excel, Igor comes with a number of functions pre-coded so that in favoable cases data can be fit without having to write a macro. However, Igor macros are not hard to write. A few templates are provided. These templates include the Michaelis-Menten function, multiple Gaussians and multiple exponentials all of which are commonly used fitting functions.
XXX FITTING FUNC MACROS HERE XXX
Baseline correction
Implications of the Planck law
- Planck's assumption places a restriction on the possible frequencies such that the energy E = nhn, where n is an integer and h is a constant. This fundamental assumption changes the nature of the problem in a fundamental way. Classically, the average energy is E = kBT. Based on a model that uses the evenly spaced set of levels one must use the averaging used by Boltzmann at low temperature. This value discussed in the section on the Partition function converts to the classical value at sufficiently high temperature.
- The Planck distribution is a bounded function with a maximum. That maximum shifts with temperature and follows the Wien displacement law. Thus, this experimental observation is satisfied by the Planck theory.
- The integrated area under the Planck curve increases with the fourth power of temperature in accord with the Stefan-Boltzmann law. This experimental observation is also explained by the Planck law.
- The fact that light is quantized implies that light has particle-like properties. The wave-particle duality is implied by the quantization of radiation.
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