Choose the correct sentence.The probability of finding the quantum particle in a volume 𝑑𝑉dV at a point (𝑥,𝑦,𝑧)(x,y,z) at time 𝑡t is given by ∣𝜓(𝑥,𝑦,𝑧;𝑡)∣2∣ψ(x,y,z;t)∣ 2 .The probability of finding the quantum particle in a volume 𝑑𝑉dV at a point (𝑥,𝑦,𝑧)(x,y,z) at time 𝑡t is given by 𝜓(𝑥,𝑦,𝑧;𝑡)𝜓⋆(𝑥,𝑦,𝑧;𝑡)𝑑𝑉ψ(x,y,z;t)ψ ⋆ (x,y,z;t)dV.𝜓(𝑥,𝑦,𝑧;𝑡)ψ(x,y,z;t) is the probability of finding the particle at the given time and position.

6.Question 6Suppose we have a particle in 1-dimension, with wavefunction 𝐴𝑒−∣𝑥∣2𝑑Ae − 2d∣x∣​ .What is the probability to find the particle in the interval [0,𝑑][0,d]?Please provide your answer in terms of 𝐴A, 𝑑d, mathematical constants such as 𝜋π (entered as 1pi) or 𝑒e (entered as 1e).(Assume that A is real)1 point0.5*(1-e^-1)A^2*d*(1-exp(-1))A^2*d*(1-e^-1)0.5*(1-exp(-1))

A particle is confined in an one dimensional box (0<x<L). The probability of finding the particle in the interval 0<x<L isa.1b.depends on the quantum number nc.depends on the energy of the particle

A particle in a central potential V (r) has a wavefunction of Ψ= f (r,Ө) sin2Ø where Ø is the azimuthal angle in the spherical polar coordinate system. Also, this wavefunction Ψ is properly normalized, i.e.˂ΨӏΨ˃=1Read the following passage to answer the given questions based on it. Choose the correct options. (Marks: 1)What is the probability of measuring Lz and obtain 2ħ?OPTIONS 0.056 0.05 0.52 0.6

For the triple integral: ∫0𝑎∫04𝑦∫0𝑔(𝑥,𝑦)𝑓(𝑥,𝑦,𝑧)𝑑𝑧𝑑𝑥𝑑𝑦what is the order at which the integral should be evaluated? Group of answer choiceswith respect to x then y then zwith respect to z then y then xwith respect to z then x then ywith respect to y then x then z

The triple integral ∫∫∫V1dV∫∫∫𝑉1𝑑𝑉 represents the volume of the region V𝑉 in 3D space.Select one:TrueFalse