Abstract
In this chapter we will introduce Dirac’s bra and ket notation and also discuss the representation of observables by linear operators. By imposing the commutation relations, we will solve the linear harmonic oscillator problem which will be used in the next chapter to study the quantized states of the radiation field. Here, we will discuss only those aspects of the bra and ket algebra which will be used later on.
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Notes
- 1.
The analysis will be based on the book by Dirac (1958a).
- 2.
In Section 9.4 we will show that when a laser is operated much beyond the threshold, it generates a coherent-state excitation of the cavity mode. It is left as an exercise for the reader to show that the operator \(\hat a^{^{\textrm{\dag}}}\) cannot have any eigenkets and similarly \(\hat a\) cannot have any eigenbras.
- 3.
Abbreviated as Tr.
References
Baym, G. (1969), Lectures on Quantum Mechanics, W.A. Benjamin, Inc., New York.
Dirac, P. A. M. (1958a), The Principles of Quantum Mechanics, Oxford University Press, London.
Ghatak, A. K., and Lokanathan, S. (2004), Quantum Mechanics, Macmillan, New Delhi.
Goldstein, H. (1950), Classical Mechanics, Addison-Wesley, Reading, Massachusetts.
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Thyagarajan, K., Ghatak, A. (2011). Vector Spaces and Linear Operators: Dirac Notation. In: Lasers. Graduate Texts in Physics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-6442-7_8
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DOI: https://doi.org/10.1007/978-1-4419-6442-7_8
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