Download presentation

Presentation is loading. Please wait.

1
**Physical Chemistry 2nd Edition**

Chapter 14 The Quantum Mechanical Postulates Physical Chemistry 2nd Edition Thomas Engel, Philip Reid

2
Objectives Introduce 5 postulates which relate to quantum mechanics.

3
**Outline The Physical Meaning Associated with the Wave Function**

Every Observable Has a Corresponding Operator The Result of an Individual Measurement The Expectation Value The Evolution in Time of a Quantum Mechanical System

4
**14.1 The Physical Meaning Associated with the Wave Function**

Postulate 1 The state of a quantum mechanical system is completely specified by a wave function The probability that a particle will be found at time t0 in a spatial interval of width dx centered at x0 is given by

5
**14.1 The Physical Meaning Associated with the Wave Function**

For sound wave, the wave function is associated with the pressure at a time t and position x. For a water wave, is the height of the wave

6
**14.1 The Physical Meaning Associated with the Wave Function**

The normalization condition for a particle confined in a 1-D space of infinite extent is Ψ(x,t) must satisfy several mathematical conditions: Wave function must be a single-valued function The first derivative must be continuous function Wave function cannot infinite amplitude over a finite interval

7
**14.2 Every Observable Has a Corresponding Operator**

Postulate 2 For every measurable property of the system in classical mechanics such as position, momentum, and energy, there exists a corresponding operator in quantum mechanics. An experiment in the laboratory to measure a value for such an observable is simulated in the theory by operating on the wave function of the system with the corresponding operator.

8
**14.2 Every Observable Has a Corresponding Operator**

All quantum mechanical operators belong to a mathematical class called Hermitian operators that have real eigenvalues.

9
**14.3 The Result of an Individual Measurement**

Postulate 3 In any single measurement of the observable that corresponds to the operator , the only values that will ever be measured are the eigenvalues of that operator.

10
**14.3 The Result of an Individual Measurement**

The measured energy values of an atom are the eigenvalues of the time-independent Schrödinger equation:

11
**14.4 The Expectation Value Postulate 4**

If the system is in a state described by the wave function , and the value of the observable a is measured once each on many identically prepared systems, the average value (also called the expectation value) of all of these measurements is given by

12
14.4 The Expectation Value As eigenfunctions form an orthonormal set, it is normalized. Thus

13
**14.5 The Evolution in Time of a Quantum Mechanical System**

Postulate 5 The evolution in time of a quantum mechanical system is governed by the time-dependent Schrödinger equation:

14
**14.5 The Evolution in Time of a Quantum Mechanical System**

We call this behavior deterministic in contrast to the probabilistic nature of Postulate 4. When time at t0, Postulate 4 applies. When t1 > t0, without carrying out a measurement in this time interval, Postulate 5 applies. If at time t1, we carry out a measurement again, Postulate 4 will apply.

Similar presentations

OK

Quantum Chemistry: Our Agenda Postulates in quantum mechanics (Ch. 3) Schrödinger equation (Ch. 2) Simple examples of V(r) Particle in a box (Ch. 4-5)

Quantum Chemistry: Our Agenda Postulates in quantum mechanics (Ch. 3) Schrödinger equation (Ch. 2) Simple examples of V(r) Particle in a box (Ch. 4-5)

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on digital media broadcasting system Animated ppt on magnetism powerpoint Ppt on e-commerce applications Ppt on law against child marriage pictures Ppt on cross site scripting vulnerability Ppt on edge detection filter Ppt on electricity from waste Ppt on cv writing Download ppt on oxidation and reduction definition Ppt on international marketing management