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Which of the following wave function is acceptable as the solution of the Schrodinger equation for all values of x?

  1. Ψ (x) = A sec x
  2. Ψ (x) = A tan x
  3. \({\rm{\Psi }}\left( x \right) = A{e^{{x^2}}}\)
  4. \({\rm{\Psi }}\left( x \right) = A{e^{ - {x^2}}}\)

Answer (Detailed Solution Below)

Option 4 : \({\rm{\Psi }}\left( x \right) = A{e^{ - {x^2}}}\)
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Detailed Solution

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Ψ (x) = A sec x and Ψ (x) = A tan x is not finite at

\(x = \frac{\pi }{2}\)

\({\rm{\Psi }}\left( x \right) = A{e^{{x^2}}}\) is not finite at x = ± ∞ ;

\({\rm{\Psi }}\left( x \right) = A{e^{ - {x^2}}}\) is finite everywhere is space. 

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