Quantum Mechanics: Theory and Applications pp 308-338 | Cite as

# Linear Harmonic Oscillator II Solutions Using Bra and Ket Algebra

## Abstract

In Chapter 7 we had solved the Schrödinger equation for the linear harmonic oscillator problem. In this chapter we will use Dirac’s bra and ket algebra to solve the same problem. Although the final results are the same, the analysis using bra and ket algebra is extremely elegant; it allows us to determine the various expectation values and also explicit expressions for the wave functions with considerable ease. The time evolution of the coherent state can also be studied in a very straightforward manner. For all this, we feel that the use of the operator algebra in solving the harmonic oscillator problem should be understood right in the beginning of the quantum mechanics course.

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### References and suggested reading

- 1.P.A.M. Dirac,
*The Principles of Quantum Mechanics*, Oxford University Press, Oxford (1958).MATHGoogle Scholar - 2.G. Baym,
*Lectures on Quantum Mechanics*, W.A. Benjamin, New York (1969).MATHGoogle Scholar - 3.H. Goldstein,
*Classical Mechanics*, Addison-Wesley Publishing Co., Reading, Massachusetts (1950).Google Scholar - 4.W.H. Louisell,
*Quantum Statistical Properties of Radiation*, John Wiley, New York (1973).Google Scholar