= Solution
<Quantum tunnelling> is penetration of, or transmission through, a finite <potential barrier> into a <classically forbidden region>, where the total <energy> is less than the <potential energy>. The <wavefunction> generally remains nonzero there, so the <Born rule> assigns a nonzero <probability> of detection. This does not require an increase in total <energy>; it is the classical relation between a definite position and a definite <kinetic energy> that cannot be imposed on the <quantum state>. For a bound <quantum harmonic oscillator>, the relevant quantity is the <probability> of finding the particle beyond its <classical turning points>; it is not an escaping transmitted beam.
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