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A particle is represented at time 
by the wavefunction, ![\[\psi(x,0)=\left{\begin{array}{cl} A(a^2-x^2),&-a\leq x \leq a\ \\0,& \mbox{otherwise}\end{array}\right.\]](https://physicshut.com/wp-content/ql-cache/quicklatex.com-018369b7d13d8fac687bce37af99e1ed_l3.png "Rendered by QuickLaTeX.com")
Where A and a are positive real constants. The normalization constant A is: ![\[A. ~~\sqrt{\frac{16}{15a^5}} ~~~B. ~~\sqrt{\frac{15}{16a^4}} ~~~C. ~~\sqrt{\frac{15}{16a^5}} ~~~D. ~~\sqrt{\frac{16}{15a^4}}\]](https://physicshut.com/wp-content/ql-cache/quicklatex.com-5af793486af8bfe2ce74b28c000e11bf_l3.png "Rendered by QuickLaTeX.com")
The correct choice is C. Watch the following video for complete solution:
The non-zero commutator brackets are: A. ![[\hat{x},\hat{p}_x]](https://physicshut.com/wp-content/ql-cache/quicklatex.com-56d7cd57850f5fd05c96961a3f53d897_l3.png "Rendered by QuickLaTeX.com")
B. ![[\hat{x},\hat{p}_y]](https://physicshut.com/wp-content/ql-cache/quicklatex.com-3c7403d9e292a5edcf0bc2e36c39d560_l3.png "Rendered by QuickLaTeX.com")
C. ![[\hat{x}^2,\hat{p}_x]](https://physicshut.com/wp-content/ql-cache/quicklatex.com-57f4df34e0152d7b8e87200a38a7123b_l3.png "Rendered by QuickLaTeX.com")
D. ![[\hat{x},\hat{p}^2_x]](https://physicshut.com/wp-content/ql-cache/quicklatex.com-aa85bd665003b4b74c49bbad7ee66381_l3.png "Rendered by QuickLaTeX.com")
The correct choices are A, C and D Watch the following video for full solution:
Suppose the 
energy level of a particle in a cubical box is given by 
, where 
is the ground state energy. Then the immediate 
energy level will be 
fold degenerate.
Keywords: IIT Bombay, Quantum Mechanics-I, Prof. P. Ramadevi, Chandigarh University, NPTEL Assignment-1, Numerical-5
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