Hilbert Space-Quantum Physics and Mechanics-Lecture Slides, Slides of Quantum Mechanics

Download Hilbert Space-Quantum Physics and Mechanics-Lecture Slides and more Slides Quantum Mechanics in PDF only on Docsity! Homework next week: • HW # 12 due Tuesday Oct 18 •No Thursday homework Announcements Quantum mechanics NO CLASS on Friday Oct 21st APS – 4C meeting Tuscon, AZ docsity.com Quantum mechanics Hilbert space N-dimensional space  1 2 3, , ,... Ne e e e Wave function are normalized: 2 ( ) 1x dx    Infinite- dimensional space  1 2 3, , ... ...n    Hilbert space: functions f(x) such as 2 ( ) b a f x dx   Wave functions live in Hilbert space docsity.com Quantum mechanics Determinate states Stationary states – determinate energy n n nH E  Generalization of Determinate state: Q q    222 2Q Q Q Q    Standard deviation:       2 †2 Q Q Q Q Q Q         For determinate state: 0  Q Q  operator eigenstate eigenvalue   0Q Q   docsity.com Quantum mechanics Quiz 15 Since any wave function can be written as a linear combination of determinate states (stationary states), for which we can write The wave function is itself a determinate state and we can write A. True B. False H H  n n nH E  docsity.com Quantum mechanics Eigenvectors & eigenvalues For a given transformation T, there are “special” vectors for which: T a a is transformed into a scalar multiple of itself a a is an eigenvector of T  is an eigenvalue of T docsity.com