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Quantum mechanical barrier problems

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  • Dekker, H.

Abstract

Three different types of quantum mechanical barrier systems are considered as eigenvalue problems. First, the real energy levels of the local ground states in a weakly biased double-well potential are determined by connecting wave functions across the barrier. For each energy level the amplitude leak through the barrier is also given. Second, the tunnelling decay rate is found as the imaginary part of the energy eigenvalues for a weakly biased local oscillator leaking through a barrier into free space. This requires connecting wave functions both across the barrier and across a harmonic turning point. Third, connecting wave functions across a linear turning point, the tunnelling decay rate is obtained for a strongly biased local oscillator. Weak and strong bias decay rates are compared for a quartic potential.

Suggested Citation

  • Dekker, H., 1987. "Quantum mechanical barrier problems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 146(3), pages 375-386.
    • Handle: RePEc:eee:phsmap:v:146:y:1987:i:3:p:375-386
    DOI: 10.1016/0378-4371(87)90274-3
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