Question

 

किसी कण का प्रसामान्यीकृत तरंग फलन निम्नलिखित है
equation$
निर्धारित करें
i) x का वह मान जिस पर प्रायिकता घनत्व फलन अधिकतम हो, और
ii) कण के equation और equation के बीच पाए जाने की प्रायिकता। 

19 Jan 2026
Answer :
Word Count : 367
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 ______ _____ _________ ___ ____ __________ ____ ________ __________.
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