MPB 8115 Lecture 26: phys 12B pancreatic and liver functions

<p>A one dimensional harmonic oscillator is changed by the addition of another force so that V= (b/x²) + &#189; m&#969;²x². One resulting wave function is &#968;= Ax^ne^{-ax^2}&#160;and d²&#968;/dx² =[n(n-1)/x²&#8211; 2a(2n+1) + 4a²x²]&#968;. Evaluate a and find E in terms of b, h and &#969;.</p>

<p>the acceleration of a marble in a certain fluid isproportional to the speed of the marble squared given bya=&#945;v^2 where v&gt;0 m/s and &#160;a=-2.15m^-1, ifthe marble enters this fluid with a speed of 2.1 m/s, how long willit take before the marble's speed is &#160;reduced to half of16s initial value?&#160;</p>
<p>a=&#945;*v^2</p>
<p>dv/dt=&#945;*v^2</p>
<p>v0=2.1m/2 (t=0)</p>
<p>Vt(t=?)=V0/2</p>
<p>dv/dt=-2.15</p>
<p>dv=-2.15v^2dt</p>

<p>Rubidium atoms are cooled to 0.16 &#956;K&#160; inan atom trap. What is their de Broglie wavelength?</p>
<p>I used&#160;&#955;=h/&#8730;(2&#960;mkT)and got 4.698x10^-7 m but it was wrong. Can't figure out for thelife of me what I did wrong. I converted mass to kg from amu, Kfrom&#160;&#956;K, and used the correct constants(6.626e-34;1.38e-23)</p>