Assigned problems for Chapter 10 on the particle in a box - Cobalt

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2. Calculate the probability that a particlewill be found between 0.49 L and 0.51L in a 1 -Dbox of length Lwhen it has (a) n =1, (b) n=2.The the wavefunction to be a constant in this rangethe wavefunctions aren = 2L sin ⎛ n x ⎞⎜ ⎟⎝ L ⎠The propability is0.51LP = ∫ n 2 dx ≈ 2 n x0.49L(a)P = 2 L sin 2 ⎛⎜⎝n xLFor x =.5L n=1⎞⎟ x⎠P= 2 L sin 2⎛⎞⎜ ⎟ x0.02L = 0.04⎝ 2⎠
3.(a) Write the Schrödinger equation <strong>for</strong> a particle in a 1-D square wellof length L(b) Calculate the expectation value of p and p 2 <strong>for</strong> a particle in the state n=1Answ:(a)− h22md 2dx 2= Ewhich has the solutionn =2L sin ⎛ n x ⎞⎜ ⎟⎝ L ⎠ˆ p = − h iddx< ˆ p >=L∫0n * p ˆn dx = 2hiL 2L ⎛sin n x ⎞∫ ⎜ ⎟⎝ L ⎠0ddx sin ⎛ n x ⎞⎜ ⎟ dx⎝ L ⎠= 2hiL 2L ⎛sin n x ⎞ ⎛∫ ⎜ ⎟ cos n x ⎞⎜ ⎟ dx = 0⎝ L ⎠ ⎝ L ⎠0
Page 4 and 5: 4. What are the most likely locatio
Page 6: (b) : = Eh = 1.603x10</stro

Assigned problems for Chapter 10 on the particle in a box - Cobalt

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