Physical Chemistry Third Edition

682 15 The Principles of Quantum Mechanics. I. De Broglie Waves and the Schrödinger Equation factor of 332958. The earth’s orbit ...

16 The Principles of Quantum Mechanics. II. The Postulates of Quantum Mechanics PRINCIPAL FACTS AND IDEAS Quantum mechanics is ...

684 16 The Principles of Quantum Mechanics. II. The Postulates of Quantum Mechanics 16.1 The First Two Postulates of Quantum Mec ...

16.2 The Third Postulate. Mathematical Operators and Mechanical Variables 685 can take on. The third and fourth postulates must ...

686 16 The Principles of Quantum Mechanics. II. The Postulates of Quantum Mechanics Theproduct of two operatorsis defined as suc ...

16.2 The Third Postulate. Mathematical Operators and Mechanical Variables 687 The following facts about commutation are useful: ...

688 16 The Principles of Quantum Mechanics. II. The Postulates of Quantum Mechanics 16.3 The Operator Corresponding to a Given V ...

16.3 The Operator Corresponding to a Given Variable 689 The operator forp^2 xmust equal the square of the operator forpx. Since ...

690 16 The Principles of Quantum Mechanics. II. The Postulates of Quantum Mechanics The operator for|L|, the magnitude of the an ...

16.3 The Operator Corresponding to a Given Variable 691 EXAMPLE16.5 For motion in thex–yplane, transform the expression forL̂zto ...

692 16 The Principles of Quantum Mechanics. II. The Postulates of Quantum Mechanics Linear Operators Quantum mechanical operator ...

16.3 The Operator Corresponding to a Given Variable 693 A hermitian operator has a set of eigenfunctions and eigenvalues. The e ...

694 16 The Principles of Quantum Mechanics. II. The Postulates of Quantum Mechanics coordinates, but the wave function vanishes ...

16.3 The Operator Corresponding to a Given Variable 695 The Eigenfunction of a Coordinate Operator Since the operator for a coor ...

696 16 The Principles of Quantum Mechanics. II. The Postulates of Quantum Mechanics 16.9 Find the complex conjugate of each of t ...

16.4 Postulate 4 and Expectation Values 697 The expectation value is the predicted mean of a set of many measurements of the var ...

698 16 The Principles of Quantum Mechanics. II. The Postulates of Quantum Mechanics If we choose a value of a constant multiplyi ...

16.4 Postulate 4 and Expectation Values 699 even if the system is in a known state. Information about this comes from part b of ...

700 16 The Principles of Quantum Mechanics. II. The Postulates of Quantum Mechanics ∫π 0 ysin^2 (y)dy 1 2 ∫π 0 y[ 1 −cos(2y)]dy ...

16.4 Postulate 4 and Expectation Values 701 Ifuis a variable that can take on any real value in a certain range, we require a fo ...