Heisenberg vs. Bandwidth Principle

Question

Is it true that the Heisenberg Uncertainty Principle is "obvious" because of the Bandwidth Theorem (Fourier Transforms)?

Answer 1

'Obvious' is a subjective term- my wife might not agree with my obvious excellent taste in ties.

However, the Heisenberg uncertainty principle is easy to understand if you are familiar with the properties of Fourier transforms. To localise a wave packet more tightly you need an increasing spread of frequency components, so there will always be a trade-off between being able to specify a location and being able to specify a frequency- it is strictly impossible to specify them both exactly for a given wave packet.