There is a significant difference in readability and usability between entering the wavefunction for the n=2 state of a harmonic oscillator as ((Alpha/Pi)^(1/4)) (1/Sqrt) (2 y^2 – 1) Exp[-y^2/2] and entering it in more mathematically-standard notation as shown to the right. This tutorial will show you how to generate expressions in standard mathematical notation that Mathematica™ will be able to interpret.
Greek Letters and Other Special Symbols
A starting point for entering specialty symbols is the Special Characters palette, shown below. Many symbols, including notably the greek letters, can be entered by clicking on them in this palette.
If you hover your cursor over one of the symbols in this palette, you will also see that many of them have <Esc> sequence aliases. For example, the Greek letter π can be entered in Mathematica with the keystroke sequence <Esc>p<Esc>. You do not need the palette open for these <Esc> sequences to work. A few of these symbols/letters have a special meaning that is pre-defined. Chief among these for our purposes are:
- (entered as <Esc>ii<Esc>): The imaginary number i, the square root of -1.
- (entered as <Esc>ee<Esc>): The constant e, the base of the natural logarithm.
- (entered as <Esc>p<Esc>): The constant pi, the ratio of a circle’s circumference to its diameter.
- (entered as <Esc>inf<Esc>): Infinity.
Most of the other letters and some of the symbols on that palette are available for use as symbol names (variables, functions, etc.). In chemistry we will use many of the Greek letters this way, as well as (entered as <Esc>hb<Esc>), which stands for the reduced Planck’s Constant.
Much of standard mathematical notation is easily entered in Mathematica™. The palette called the Basic Math Assistant contains a mouse-oriented way to enter most of these, and as with the letters/symbols described above, hovering the mouse over a particular template will show you keyboard shortcuts to enter many of these structures quickly. The most important of these are described below:
- Fractions: The forward slash symbol (/) is used traditionally to denote division. <Ctrl>/ creates a fraction.
- Exponents: The carat symbol (^, found over the 6 key on a standard keyboard) is used traditionally to denote exponentiation. <Ctrl>6 creates an exponent.
- Roots: <Ctrl>2 creates a square-root symbol. <Ctrl>5 from inside the root will let you specify roots other than square.
- Subscripts: <Ctrl>- creates a subscript. There are a few places where subscripts are useful, but they also can be problematic in some contexts, so be cautious with their use.
- Getting out of Fractions, Exponents, Etc.: <Ctrl><Spacebar> move the cursor one level out of the current structure.
- Integration: <Esc>int<Esc> creates an integral symbol. You can add limits by typing <Ctrl>- to get to the lower limit, and then while in the lower-limit typing <Ctrl>5 to get to the upper limit. After typing <Ctrl><Spacebar> to get back to the main line, you add the differential with <Esc>dd<Esc>.
Finally, Mathematica™ operates under the standard mathematical convention that a space indicates multiplicaiton.