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We analyse the limit to tree height by employing elementary quantum mechanics. The xylem is assumed as a one-dimensional vertical potential well without any rigid walls; transporting a water molecule in an oscillating medium. A macromolecule with coherence can behave quantum mechanically. By applying the quantization rule of the Wentzel–Kramers–Brillouin approximation of the Schrödinger equation to the Bernoulli equation, a general quadratic equation on the limit of the tree height is derived. The limit of tree height is therefore calculated to range from 0 to 203.87 m, and approaches the peak value of 101.94 m (as the quantum number increases).

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Theoretical Calculation of the Tree Structure Height Limit by WKB Approximation of the Schrödinger Equation

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  • 发表日期：

    2025年

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  • John Jabaraj Devadason

摘要

We analyse the limit to tree height by employing elementary quantum mechanics. The xylem is assumed as a one-dimensional vertical potential well without any rigid walls; transporting a water molecule in an oscillating medium. A macromolecule with coherence can behave quantum mechanically. By applying the quantization rule of the Wentzel–Kramers–Brillouin approximation of the Schrödinger equation to the Bernoulli equation, a general quadratic equation on the limit of the tree height is derived. The limit of tree height is therefore calculated to range from 0 to 203.87 m, and approaches the peak value of 101.94 m (as the quantum number increases).