(Answered) 1 find the order of the group of transformations that

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1. Find the order of the group of transformations that leaves an equilateral triangle invariant. Identify the complete set of group elements, find a matrix representation, and then construct the multiplication table. What is the common name of this group?

2. Show that the two expressions below are equivalent.

1508_What conditions are necessary for this equivalence.png

What conditions are necessary for this equivalence?

3. Derive the position-momentum Heisenberg Uncertainty Principle. What is the value of ΔxΔp_x for the Gaussian wave packet

2262_What conditions are necessary for this equivalence1.png

Suppose the variance, cr² is the complex number oi + io-?, then what is the value of axagi_s (be careful about normalization)? What is the solution to the Schrodinger equation of a free particle if 0(x) is taken as the initial condition 0(x, t = 0)?

4. For the wave function, ii)(x) = c_o exp(ip_ox/h)/1/4² + x², find the normalization constant c_o and the probability of finding the particle in the interval ±a//5. What is the mean momentum?

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