Q6 / 160 · AP EAMCET 2020 (18 Sep Shift 2) · Chemistry

Which among the following represents Schrodinger wave equation?

  • A
    \(\frac{d^2 \psi}{d x^2}+\frac{d^2 \psi}{d y^2}+\frac{d^2 \psi}{d z^2}+\frac{4 \pi m}{h}(E-v) \psi=0\)
  • B
    \(\hat{H}=\frac{h}{4 \pi^2 m}\left(\frac{d^2}{d x^2}+\frac{d^2}{d y^2}+\frac{d^2}{d z^2}\right)+V\)
  • C
    \(\hat{H}=\frac{-h^2}{8 \pi^2 m}\left(\frac{d^2}{d x^2}+\frac{d^2}{d y^2}+\frac{d^2}{d z^2}\right)+P\)
  • Correct answer
    D
    \(\frac{d^2 \psi}{d x^2}+\frac{d^2 \psi}{d y^2}+\frac{d^2 \psi}{d z^2}+\frac{8 \pi^2 m}{h^2}(E-V) \psi=0\)

Solution

The Schrondinger wave equation is \(\frac{d^2 \psi}{d x^2}+\frac{d^2 \psi}{d y^2}+\frac{d^2 \psi}{d z^2}+\frac{8 \pi^2 m}{h^2}(E-V) \psi=0\) (where, \(\psi=\) wave function, \(m=\) mass of electron, \(h=\) Planck's constant, \(E=\) total energy of electron, \(V=\) potential energy of electron)

Hence, the correct answer is option: 'D'.

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