Word Count : 367

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कण का प्रसामान्यीकृत तरंग फलन दिया है: [ \psi(x) = \begin{cases} 2a \sqrt{a} , x , e^{-ax}, & x > 0 \ 0, & x < 0 \end{cases} ] i) प्रायिकता घनत्व अधिकतम होने का स्थान: प्रायिकता घनत्व (P(x) = |\psi(x)|^2) होता है। अतः, (x>0) के लिए: [ P(x) = |\psi(x)|^2 = \left(2a \sqrt{a} , x , e^{-ax}\right)^2 = 4 a^3 x^2 e^{-2ax} ] अधिकतम ढूँढने के लिए ( \frac{dP}{dx} = 0 ) करें: [ \frac{d}{dx} \left(4 a^3 x^2 e^{-2ax} \right) = 4 a^3 \frac{d}{dx} \left( x^2 e^{-2ax} \right) ] उत्पन्न __________ _______ __________ _____ ___ ______ _________ _______ ________ ______.
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