More intense more density of photons more probability

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Chapter 6 / Exercise 1
Biology: The Dynamic Science
Hertz/Russell
Expert Verified
more intense = more density of photons = more probability of finding a photon in a specific volume - Complex conjugate : where ever you see i, make it negative i - Probability = ψ ^2 = ψ * times ψ - Normalization - In any system, the probability that the particle is SOMEWHERE is 100% = 1 - For the normalized 1-dimensional wave function: ψ (x) - integral of probability from negative infinity to positive infinity = 1 - For the un-normalized 1 dimensional wave function, the same ^^^ equals C.
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Chapter 6 / Exercise 1
Biology: The Dynamic Science
Hertz/Russell
Expert Verified
We don ʼ t know how to normalize, but know conceptually Schrodinger Equation Applications - Particle in a box - end on the node - y = sin (n π x/L) -> quantization, only certain numbers are allowed! - normalizing factor : changing the amplitude of the curves - energy goes up by n^2 - probability: where the particle is likely to be - Zero point energy - lowest allowed energy - you have to start with one because the probability would be zero, meaning the particle isn ʼ t even in the box - Correspondence principle - Quantum mechanics gives the same result as classical theory in the limit of very large quantum numbers - Equal probability of finding the particle everywhere in the box - Quantum harmonic oscillator - A mass (m) on a frictionless surface attached to a spring with a stiffness (k) - Restoring force (F(x) = - k*x) - Potential energy is negative work done on mass by spring - The same concepts can be used with atoms vibrating - k is the bond strength - Quantization - only certain vibrations are allowed - Zero Point Energy: - The lowest allowed energy is 1/2hv even when n=0 - Translation has stopped, but there is still vibrating - Even at n=0 there is a finite energy, the atoms are still vibrating even at T = 0K - Supports the Heisenberg uncertainty principle - Correspondence Principle - Quantum Mechanics gives the same result as classical theory in the limit of very large quantum numbers - starts to match the classical probability as n increases - Atoms - Hydrogen Atom - One proton in nucleus, one electron - easiest atom - Because they are special atoms, they have spherical potential and therefore spherical coordinates - x, y, z, - othogonal coordinate system - r, θ , Φ - orthogonal coordinate system (1:1 correspondence with xyz) - r = interparticle distance - θ = angle from z-axis - Φ = angle from x- axis in xy plane - Energy is dependent on the r = matches the Bohr modeling - The smaller n is, the lower the energy of the electron
- The smaller n is, the smaller the orbital - Angular momentum quantum number distinguishes “sub shells” within a given shell that have different shapes - magnetic quantum number - distinguishes orbitals within given sub-shells that have different orientations in space
One- Electron Atoms - if all three spatial quantum numbers are given - orbital, called “state” - Energy depends on quantum number n (ONLY FOR ONE-ELECTRON) - states with different values for t & m are degenerate - degenerate states have different quantum numbers but exactly the same energy Size/Shape or Orbitals - 2 Dimensions - x, y, z Cartesian Coordinates - For constant dx and dy, the area in xy plane is the same - dx * dy = area - r, θ , Φ Coordinates -