2.1 Evaluate the constant B in the hydrogen-like wave function Y(1,0,0)=Br²sin²0e²¹⁹ exp(-3Zr/3a) 2.2 The wavefunction of a state of harmonic oscillator is given by: 1/4 Φ(x) = mo 64πħ 4mo ħ ²x² −2)exp(-m cox ²/2ħ); - 00

1. Given the following probability density function: p(x) = Ae¬^(x-a)². 2. A particle of mass, m, has the wavefunction given by: Þ(x,t) = Ce-a[(mx²/h) + it] . 3. In a few sentences, explain why it is impossible to calculate (p) in the first problem, whereas in the second problem this is straightforward. Highlight the key concepts that differentiate these problems.

In the following questions, we will use quantum states made up of the hydrogen energy eigenstates: Q1: Consider the election in a hydrogen atom to initially be in the state: F A. B. C. a) What is the probability of measuring the energy of this state and obtaining E₂? √3 √ vnim (r0,0)=R(r)Y," (0,0) always Y(t = 0) = √3 R₁OYO at t=0 but something different at t>0 ² at t=0 but something different at t>0 D. always 3 + E. Something else. b) Explain your answer. R₂₁ + R32Y₂¹

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