Using the expectation values from the previous questions, show that the eigenfunctions for the particle in a box obey theHeisenberg uncertainty for position and momentum, where we define the uncertainties statistically using standarddeviations as follows:  222 2 2222 2 2( )* ] ( ) ( )* ( )( )*[ ] (]) ( )*[ ] (ˆ ˆ[ [ˆ ˆ )xpx x x xx x xx x x dx x dxp p p d xx dxp           (a)And writing the Heisenberg uncertainty for position and momentum as2x x px p    Note that you need the square roots of the quantities defined in (a).Show that1/2 1/22 2a 2 2 1.136 / 22 3 a 2 3 2x x px p                             ħħħħ[5 marks]

Discuss the prohibition of E = 0 for a particle trapped in a box L wide in terms of the uncertainty principle. How does the minimum momentum of such a particle compare with the momentum uncertainty required by the uncertainty principle if we take Delta*x =L?

A particle in a one dimensional infinite square well (box) is in a superposition of two quantum states:1 21234   where1 2and  are orthogonal, normalized (ortho-normal) eigenfunctions of the Hamiltonian.(a) Calculate the new normalization constants for1 2and  . [2 marks](b) A measurement of energy is made. What is the probability that the measurement will find energy1E ?What is the probability that the measurement will find energy2E ? [2 marks](c) Write down the integral expression for the evaluation of the expectation value of position,x - evaluateany “trivial” integrals, but leave as integrals any that require a full solution. [2 marks](d) Write down the integral expression for the evaluation of the expectation value of momentum,xp -evaluate any “trivial” integrals, but leave as integrals any that require a full solution

The entire information of a quantum system can be gathered with the help of(a) position (b) eigen value(c) momentum operator (d) wave function

The wave function for a quantum particle is given by𝜓(x)= Axbetween x = 0 and x = 1.00, and 𝜓(x) = 0 elsewhere.Find the value of the normalisation constant A.Answer for part 1 Find the expectation value of the particle's position.Answer for part 2Find the probability that the particle will be found between x = 0.245 and x = 0.465.

Heisenberg uncertainty principle has no significance in our everyday life. Explain?