Physical Chemistry Third Edition

662 15 The Principles of Quantum Mechanics. I. De Broglie Waves and the Schrödinger Equation If a system consists ofnparticles m ...

15.3 The Particle in a Box and the Free Particle 663 which are generally shared by waves: (1)the wave function is single-valued, ...

664 15 The Principles of Quantum Mechanics. I. De Broglie Waves and the Schrödinger Equation (a) (b) 0 0 t vx x Figure 15.3 Mech ...

15.3 The Particle in a Box and the Free Particle 665 where κ^2  2 mE h ̄ 2 (15.3-5) Equation (15.3-4) is of the same form as Eq ...

666 15 The Principles of Quantum Mechanics. I. De Broglie Waves and the Schrödinger Equation 0.0 Energy or wave function value E ...

15.3 The Particle in a Box and the Free Particle 667 The energy of a de Broglie wave is inversely proportional to the square of ...

668 15 The Principles of Quantum Mechanics. I. De Broglie Waves and the Schrödinger Equation The Time-Dependent Wave Function fo ...

15.3 The Particle in a Box and the Free Particle 669 For example, when a photon is absorbed or emitted by a molecule, the initia ...

670 15 The Principles of Quantum Mechanics. I. De Broglie Waves and the Schrödinger Equation whereCis a constant and where the q ...

15.3 The Particle in a Box and the Free Particle 671 of massmcan move only parallel to thexaxis, the time-independent Schrödinge ...

672 15 The Principles of Quantum Mechanics. I. De Broglie Waves and the Schrödinger Equation and a frequency given by ν 2 πE h ...

15.3 The Particle in a Box and the Free Particle 673 whereκ^2 is the square of the magnitude of the wave vector. As in the one-d ...

674 15 The Principles of Quantum Mechanics. I. De Broglie Waves and the Schrödinger Equation ∫∞ −∞ ψ 2 (x)ψ 3 (x)dx 0 b.Work ou ...

15.4 The Quantum Harmonic Oscillator 675 Eq. (14.2-32). If we set the constantV 0 equal to zero, the time-independent Schrödinge ...

676 15 The Principles of Quantum Mechanics. I. De Broglie Waves and the Schrödinger Equation relation pick the other values, the ...

15.4 The Quantum Harmonic Oscillator 677 Solution a. ∆EE 2 −E 1  3 2 hν− 1 2 hνhν h 2 π √ k m ν 1 2 π √ k m b.The frequency ...

678 15 The Principles of Quantum Mechanics. I. De Broglie Waves and the Schrödinger Equation 23 0 1 Energy/ hn or wave function ...

15.4 The Quantum Harmonic Oscillator 679 EXAMPLE15.7 Find the classical amplitude of vibration of a hydrogen molecule with an en ...

680 15 The Principles of Quantum Mechanics. I. De Broglie Waves and the Schrödinger Equation d.Express the value ofψ^22 in terms ...

15.4 The Quantum Harmonic Oscillator 681 whereEis the energy of the system,ψis a wave function, andĤis the Hamiltonian operator ...