![]() They must have the same energies as $\psi_1$ and $\psi_2$. That means that, from what we've talked about earlier, $-\psi_1$ and $-\psi_2$ must also be (approximations of) solutions to the Schrödinger equation. We already said that $\psi_1$ and $\psi_2$ are (approximations of) solutions to the Schrödinger equation. P2 is the partial pressure of the liquid at T2. Now let's talk about those combinations that we missed out. The change in vapor pressure of a pure substance as temperature changes can be described using the equation known as the Clausius-Clapeyron Equation: lnP2 P1 Hvap R ( 1 T1 1 T2) (1) (1) l n P 2 P 1 H v a p R ( 1 T 1 1 T 2) Where: P1 is the partial pressure of the liquid at T1. These are the bonding and antibonding orbitals respectively (at least, to within a normalisation constant, which I'm not going to care about here because the details are irrelevant). Now, from what you already know, you can get two molecular orbitals $\psi_1$ and $\psi_2$: So, let's assume for simplicity's sake that their phases are both positive. From the previous sections, we have already established that as far as the hydrogen atom is concerned, the individual phases of $\phi_1$ and $\phi_2$ do not matter. Let's call the 1s orbital of the hydrogen on the left $\phi_1$ and the 1s orbital of the hydrogen on the right $\phi_2$. ![]() One way to find approximate forms of the MOs is to make linear combinations of atomic orbitals this method is called the LCAO approximation. ![]() The proper way to find the molecular orbitals is to solve the Schrödinger equation for the entire system, which is really difficult to do. However, let's say for a particle in a box, if you solve the momentum operator for the $n^\text$ molecule. According to the Copenhagen interpretation of quantum mechanics, \Psi2 is the 'probability density' (the probability per volume of finding a particle, such as an electron, in a given volume, in the limit the volume approaches zero). Pounds per square inch (PSI) is the pressure that results when a 1-pound force is applied to a unit area of 1 square inch. Another way to describe an ideal gas is to describe it in mathematically. Lastly, the constant in the equation shown below is R, known as the the gas constant, which will be discussed in depth further later: PV nRT (2) (2) P V n R T. ![]() So having a negative wavefunction doesn't mean anything physically. The four gas variables are: pressure (P), volume (V), number of mole of gas (n), and temperature (T). The wavefunction of a particle actually has no physical interpretation to it until an operator is applied to it such as the Hamiltonian operator, or if you square it which gives its probability of being at a certain place. ![]()
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