Question

What is the relation of energy with respect to to lower no. Of nodes in wave function?

Answer 1

The lowest energy level (ground state) has no nodes, and each energy level higher adds a node. This is only true for bound states. Free particles has infinitely many nodes. The wavenumber (number of wavelengths per unit distance) of a free particle is proportional to the momentum of the particle. Nodes occur when there’s some amount of the wave going one direction and some amount of it going the other direction. In one dimension, this looks like A*exp(ikx) + B*exp(-ikx), where k is the wavenumber

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Answer 2

QUESTION:

⠀⠀⠀⠀⠀⠀⠀ What is the relation of energy with respect to to lower no. Of nodes in wave function?

ANSWER:

⠀⠀⠀⠀⠀⠀The lowest energy level (ground state) has no nodes, and each energy level higher adds a node. This is only true for bound states. Free particles has infinitely many nodes. The wavenumber (number of wavelengths per unit distance) of a free particle is proportional to the momentum of the particle. Nodes occur when there’s some amount of the wave going one direction and some amount of it going the other direction. In one dimension, this looks like A*exp(ikx) + B*exp(-ikx), where k is the wavenumber

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