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The Chemical Educator

ISSN: 1430-4171 (electronic version)

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Abstract Volume 8 Issue 4 (2003) pp 238-240

Residual or Zero-Point Energy in Quantum Systems: Another View for Two Well-known Cases

Fernando Enríquez and Jose J. Quirante*

Departamento de Química Física, Facultad de Ciencias, Universidad de Málaga, Campus de Teatinos s/n. 29071- Málaga, Spain,
Received February 25, 2003. Accepted April 21, 2003.

Published online: 14 July 2003

Abstract. From the mathematical form of Heisenberg's uncertainty principle and the exact solutions for both the particle in a box and the harmonic oscillator models, we derive simple but rigorous proofs of the existence of zero-point energies for these quantum systems. Such demonstrations may help students in their understanding of this general quantum property.

Key Words:  In the Classroom; physical chemistry; quantum theory; zero-point energy

(*) Corresponding author. (E-mail:

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Issue date: August 1, 2003

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