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Additional resources for Ionic Mobilities in Ammonia-Hydrogen Mixtures and an Anomalous Effect of Ammonia
Example text
E. observables) are real. 6. 5, any hermitian operator, signifies a mathematical operation to be done on a wavefunction, which will yield a constant, o, if the wavefunction is an eigenfunction of the operator. Next the complex conjugate of the wavefunction, sides of Equation 2-21 and integrated over all space. is multiplied to both If the wavefunction is normalized, then the integral is equal to one as shown in Equation 2-9. This leads directly to the value of the constant o. 28 Chapter 2 As mentioned previously, the constant o corresponds to some physically observable quantity such as position, momentum, kinetic energy, or total energy of the system, and it is called the expectation value.
The normalized wavefunction and the energy for the particle in a onedimensional box are as follows For a given system, the mass of the particle and the dimensions of the box are all a constant, k. Note that the energy difference between each energy level increases with increasing value of n. 24 Chapter 2 Fundamentals of Quantum Mechanics 25 Note that quantization of the energy states for the particle has occurred due to the potential energy of the system. Only those states that will result in nodes in the wavefunction at the two walls of the box are allowed.
The Hamiltonian in Equation 3-1 can now be written in terms of r and Since the radius r is constant in this problem, all of the terms that involve derivatives with respect to r will be zero, reducing the Hamiltonian to just one variable, The moment of inertia, I, of the particle, is equal to its mass times the square of the radius of gyration r. 4). This will result in the same functional forms for the wavefunctions in terms of the variable The following wavefunction will be used: The constants A and B are normalization constants, and the constant k will be determined by the boundary conditions for the particle.
Ionic Mobilities in Ammonia-Hydrogen Mixtures and an Anomalous Effect of Ammonia
by Edward
4.3