This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Physical Chemistry Course Number: C362 1 The mathematical ideas you will encounter while learning quantum mechanics We first outline a few mathematical ideas that one needs to tackle quantum me chanics. This section includes a brief review of: Vectors and matrices Differentiation and integration Complex numbers 1.1 Vectors and matrices 1. We will start with simple concepts from threedimensional vector spaces. 2. In 3D, a vector has three components: vector r = x i + y j + z k. (1.1) Here, i , j and k are unit vectors in the x, y and z directions respectively. i , j and k may also be called basis vectors or just bases and this is a terminology that we will use often. Vectors can be represented in the following form: vector r x y z (1.2) 3. A vector is fully described by: (i) its magnitude, and (ii) its direction. Com pare this with a scalar number that only has magnitude. 4. The magnitude of the vector vector r can be calculated by using the concept of a dot product:  vector r  vector r vector r = radicalBig  x  2 +  y  2 +  z  2 (1.3) where we have introduced the definition of the dot product of two vectors: vectora = a 1 i + a 2 j + a 3 k vector b = b 1 i + b 2 j + b 3 k vectora vector b = a 1 b 1 + a 2 b 2 + a 3 b 3 (1.4) Chemistry, Indiana University 4 c circlecopyrt 2011, Srinivasan S. Iyengar (instructor) Physical Chemistry Course Number: C362 5. The dot product is a very fundamental concept, and very useful for our further development. Physically a dot product of vectora with vector b is equal to the magnitude of vectora times the projection of vector b onto vectora . See figure on board....
View
Full
Document
 Winter '11
 AmarFlood

Click to edit the document details