BioPHYSICAL chemistry
that are quantized. The mathematical analysis for solving the equation is provided in Derivation box 11.1. The reader may skip t ...
Properties of the solutions The quantum-mechanical problem was solved by substituting the potential for the simple harmonic osci ...
into Schrödinger’s equation, yielding (11.11) As shown above, this second-order differential equation is called the Hermite equa ...
We can check the solutions for all values of xby substituting the dif- ferent solutions into Schrödinger’s equation. For example ...
There are a total of four terms in the equation. Two are multiplying x^2 (the terms in the left-hand parentheses) and can be rew ...
The probability, P, of finding the mass outside the classically allowed region is then: (11.26) The value of yAis given by: (11. ...
Let us determine what energies and wavelengths are relevant for transi- tions between adjacent energy states. Consider a proton ...
compared to the same group that does not have the hydrogen bond. Because the secondary structure has well-defined hydrogen-bondi ...
Now consider the molecule with the isotopic substitution^13 C^16 O: (11.42) (11.43) The change in frequency due to the isotope s ...
the point where the electrons and protons are delivered. The composition of this cofactor differs for the two types of enzyme, c ...
The molecular structure of the H cluster represented a new type of bioinorganic cluster. The involvement of two toxic compounds, ...
Problems 11.1 Write the smallest energy that the oscillator can have in terms of kand m. 11.2 Write the zero-point energy for an ...
11.7 Calculate the vibrational frequency for a proton if k=600Nm−^1. 11.8 For a^12 C^16 O bond, if k=500Nm−^1 calculate (a) the ...
(b) Write Schrödinger’s equation for ethene using the harmonic oscillator approximation. (c) Write (but do not solve) the probab ...
The primary motivation in studying quantum mechanics is that the key constituents of biochemical reactions, namely electrons, ha ...
where ris the distance between the electron and nucleus, ε 0 is the vacuum permittivity, −eis the electron charge, and +eis the ...
240 PART 2 QUANTUM MECHANICS AND SPECTROSCOPY Substitution of this into the Schrödinger equation gives: (db12.6) Now, multiply b ...
CHAPTER 12 THE HYDROGEN ATOM 241 Now let us use the separation of variables again. Define: Y(θ,φ) =Θ(θ)Φ(φ) (db12.14) After subs ...
242 PART 2 QUANTUM MECHANICS AND SPECTROSCOPY The values of the constant mlare fixed by the physical constraint that, if the obj ...
CHAPTER 12 THE HYDROGEN ATOM 243 This will be true if l=0 and ml=0. Another possible solution is: Θ(θ) =Bcosθ (db12.28) Substitu ...
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