Physical Chemistry Third Edition

722 16 The Principles of Quantum Mechanics. II. The Postulates of Quantum Mechanics it was established that if the state just be ...

16.6 Postulate 5. Measurements and the Determination of the State of a System 723 e.Measurement of the energy of a particle in a ...

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17 The Electronic States of Atoms. I. The Hydrogen Atom PRINCIPAL FACTS AND IDEAS The hydrogen atom is an example of a central- ...

726 17 The Electronic States of Atoms. I. The Hydrogen Atom 17.1 The Hydrogen Atom and the Central Force System The hydrogen ato ...

17.1 The Hydrogen Atom and the Central Force System 727 wherevcandvare the velocity of the center of mass and the relative veloc ...

728 17 The Electronic States of Atoms. I. The Hydrogen Atom In previous chapters we used a capitalΨto represent a time-dependent ...

17.2 The Relative Schrödinger Equation. Angular Momentum 729 EXAMPLE17.1 The electron mass is 9. 10939 × 10 −^31 kg and the prot ...

730 17 The Electronic States of Atoms. I. The Hydrogen Atom Equation (17.2-1) is a partial differential equation with three inde ...

17.2 The Relative Schrödinger Equation. Angular Momentum 731 Substitution ofΘ(θ)Φ(φ) into Eq. (17.2-7) followed by division byΘ( ...

732 17 The Electronic States of Atoms. I. The Hydrogen Atom This function is an eigenfunction of̂Lzwith eigenvaluehm ̄ ifBis cho ...

17.2 The Relative Schrödinger Equation. Angular Momentum 733 TheΘFunction After replacement of the last term on the left-hand si ...

734 17 The Electronic States of Atoms. I. The Hydrogen Atom Table 17.1 Normalized Spherical Harmonic FunctionsYlm(θ,φ) Θlm(θ)Φm ...

17.2 The Relative Schrödinger Equation. Angular Momentum 735 TheYlmfunctions and the possible values ofL^2 andLzare the same for ...

736 17 The Electronic States of Atoms. I. The Hydrogen Atom Exercise 17.4 Transform the expression forΘ 11 Φ 1 xto Cartesian coo ...

17.3 The Radial Factor in the Hydrogen Atom Wave Function. The Energy Levels of the Hydrogen Atom 737 where we now omit the subs ...

738 17 The Electronic States of Atoms. I. The Hydrogen Atom From the first relation in Eq. (17.3-4), the energy is quantized and ...

17.3 The Radial Factor in the Hydrogen Atom Wave Function. The Energy Levels of the Hydrogen Atom 739 In the (fictitious) limit ...

740 17 The Electronic States of Atoms. I. The Hydrogen Atom We have used the fact that the sum of a set of consecutive integers ...

17.4 The Orbitals of the Hydrogen-Like Atom 741 PROBLEMS Section 17.3: The Radial Factor in the Hydrogen Atom Wave Function. The ...