Available online
Description
The programme demonstrates that wave packets can be envisaged as being compounded of various sinusoidal waves and that the Fourier transformation is a limiting case of a Fourier series.
The programme demonstrates that wave packets can be envisaged as being compounded of various sinusoidal waves and that the Fourier transformation is a limiting case of a Fourier series.
| Module code and title: | SM351, Quantum theory and atomic structure |
|---|---|
| Item code: | SM351; 03 |
| First transmission date: | 01-04-1974 |
| Published: | 1974 |
| Rights Statement: | |
| Restrictions on use: | |
| Duration: | 00:24:30 |
| + Show more... | |
| Producer: | Ted Smith |
| Contributors: | Tom B. Smith; Russell Stannard |
| Publisher: | BBC Open University |
| Keyword(s): | Fourier analyser; Fourier series; Fourier transformation; Frequency spectrum; Ripple tank experiment; Sinusoidal waves; Wavepackets |
| Footage description: | Russ Stannard introduces the programme, Stannard uses animated diagrams to demonstrate that various wave forms are built up from the sums of different sine waves. Wave packets result when sufficient waves have been summed. Smith demonstrates that a general series of wave packets can be expressed as a sum of various sine waves. He uses a mathematical approach, that of Fourier series. The mathematics are captioned. Stannard, with analyser equipment and a wave synthesiser, demonstrates how a frequency spectrum for an isolated wave packet can be inferred. He examines the frequency spectrum of repeating wave packets. Stannard explains how a single, isolated wave packet can be obtained by going through some progressive Fournier series to a limit. A frequency spectrum is built up to illustrate his points. Tom Smith provides the mathematical framework for this approach to a limit. Several captions are used as visual aids. A computer animation illustrates the transformation. Stannard and Smith develop the idea of moving wave packets. The simple wave equation is used to model moving, unchanged wave packets. They then examine moving wave packets with changing profiles. Moving waves in a ripple tank are used to illustrate points in the discussion. Smith goes through the mathematics of moving wave packets. Computer animations show a solution to Schrodinger's equation for a free particle in the form of wave packets which move in a line and change their shape. More shots of waves in ripple tank. |
| Master spool number: | 6HT/71202 |
| Production number: | 00525_1140 |
| Videofinder number: | 1043 |
| Available to public: | no |
