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Which of a, b or c is most likely to be correct? J Hint: Romombor tho roguirod rtiog of rono

Which of a, b or c is most likely to be correct? J Hint: Romombor tho roguirod rtiog of rono

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I think the answer is B and C. but I'm confused single-valued function and normalizable(finite) function. Could you please explain them in detail?

Thank you very much

Potential wavefunctions for a 1-d system have been suggested. They are a. V(x) N tan(ax) for 0 < x < ∞ and N and a are con- stants. b. V(x) Nx/²e¬ax for 0 < x < ∞ and N and a are con- stants. c. V(x) Which of a, b or c is most likely to be correct? Justify your answers. Hint: Remember the required propoerties of wavefunctions from our discussion of postulate 1: N sin(ax) for 0 < x < ∞ and N and a are constants. 1. They must be single valued 2. They must 3. They must be normalizable, i.e. continuous dx V* V (2.2) 0, must be finite: it's a probability density.
Transcribed Image Text:Potential wavefunctions for a 1-d system have been suggested. They are a. V(x) N tan(ax) for 0 < x < ∞ and N and a are con- stants. b. V(x) Nx/²e¬ax for 0 < x < ∞ and N and a are con- stants. c. V(x) Which of a, b or c is most likely to be correct? Justify your answers. Hint: Remember the required propoerties of wavefunctions from our discussion of postulate 1: N sin(ax) for 0 < x < ∞ and N and a are constants. 1. They must be single valued 2. They must 3. They must be normalizable, i.e. continuous dx V* V (2.2) 0, must be finite: it's a probability density.
Expert Solution
Step 1

Wavefunctions

Wavefunctions are mathematical functions that encode the properties of a particle. The values of all the observables are present in the wavefunction of the particle. In Quantum Mechanics, the wavefunction is generally represented by the Greek letter ψ.

The wavefunction satisfies an equation known as Schrodinger's equation. In one dimension the Schrodinger's equation is expressed as

-ħ22m∂2ψ∂x2+Vψ=Eψ

V is the potential energy of the particle and E is known as the energy eigenvalue.

 

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