class31

# class31 - Today more about When is small small enough for...

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Today: more about “When is small ‘small enough’ for QM”? Check your current clicker score on CUlearn. If you have no score you didn’t register your clicker correctly. Look at energy level spacing compared to thermal energy, k B T= ~25 meV at room temp. k B = Boltzmann’s constant 0 L ? E Use time independ. Schrod. eq. Last class : Energy levels for electron in short wire Step 1: Figure out V(x Then: figure out how to solve, and what solutions mean physically. ) ( ) ( ) ( ) ( 2 2 2 2 x E x x V x x m ψ ψ ψ = + h Want this to be ~25 meV. What L do we need? Remember: for atoms L very small (~a B ); barb2right spacing very large (several eV) E Step 1 (solving Schr. eqn) : Figure out V(x) What is V(x) of this wire? x Depth of the potential = Energy needed to remove the electron from the metal = work function Φ. ( Φ ~ 4.7 eV for copper) Reasoning to simplify how to solve. Electron energy not much more than ~kT=0.025 eV. Where is electron likely to be? mathematically V(x) = 4.7 eV for x<0 and x>L V(x) = 0 eV for 0>x<L 0 eV 0 L 4.7 eV What is the chance it will be outside of the well? x Q1 A. zero chance B. very small chance (<50% chance) C. 50:50 chance D. very likely (>50% chance) E. 100% chance it will be outside of the well mathematically V(x) = 4.7 eV for x<0 and x>L V(x) = 0 eV for 0<x<L 0 eV 0 L 4.7 eV What does that say about boundary condition on ψ (x) ?

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