1. Quantum One: Lecture 11

3. The Position and the Momentum Representation

13. Similarly, we find that, since then so that and are Fourier transform pairs. Note and know where the plus and minus signs go!

14. Similarly, we find that since then so that and are Fourier transform pairs. Note and know where the plus and minus signs go!

15. Similarly, we find that since then so that and are Fourier transform pairs. Note and know where the plus and minus signs go!

16. Similarly, we find that since then so that and are Fourier transform pairs. Note and know where the plus and minus signs go!

17. Similarly, we find that since then so that and are Fourier transform pairs. Note and know where the plus and minus signs go!

18. Similarly, we find that since then so that and are Fourier transform pairs. Note and know where the plus and minus signs go!

19. Similarly, we find that since then so that and are Fourier transform pairs. Note and know where the plus and minus signs go!

20. Similarly, we find that since then so that and are Fourier transform pairs. You should note carefully where the plus and minus signs go!

22. In finishing up our discussion of the first postulate, it is useful to explicitly gather together the important relations regarding the position and momentum representation, which allows the symmetry between them to be appreciated.

23. Continued:

24. We often work on problems that involve motion only in one dimension, for which the following analogous relations hold:

25. We have completed our discussion of the first postulate of the general formulation of quantum mechanics, and illustrated its structure by using our general formal definitions about state vectors in quantum mechanical state space, to re-derive properties that were familiar to use from Schrödinger's mechanics for a single quantum particle. In the next lecture, we begin a discussion of the second postulate, which provides information about the nature of observables of general quantum mechanical systems.

26. We have completed our discussion of the first postulate of the general formulation of quantum mechanics, and illustrated its structure by using our general formal definitions about state vectors in quantum mechanical state space, to re-derive properties that were familiar to use from Schrödinger's mechanics for a single quantum particle. In the next lecture, we begin a discussion of the second postulate, which provides information about the nature of observables of general quantum mechanical systems.