Summarize the following:
A wave function or wave function is a mathematical tool in quantum mechanics that describes the quantum state of a particle or system of particles. It is commonly applied as a property of particles relating to their wave-particle duality, where it is denoted ψ(position,time) and where |ψ|2 is equal to the chance of finding the subject at a certain time and position.  For example, in an atom with a single electron, such as hydrogen or ionized helium, the wave function of the electron provides a complete description of how the electron behaves. It can be decomposed into a series of atomic orbitals which form a basis for the possible wave functions. For atoms with more than one electron (or any system with multiple particles), the underlying space is the possible configurations of all the electrons and the wave function describes the probabilities of those configurations. In solving homework problems involving the wave function, familiarity with complex numbers is a prerequisite. Other prerequisites include the math of linear algebra, Euler's formula from complex analysis and the bra–ket notation.

summary: Learn about wave function.


Summarize the following:
The satin or gloss finish will protect the gutters from water damage. An oil-based top coat will dry more quickly and leave a more even application. Buy top coat for the gutters at your local hardware store or online. Most homeowners will go for classic white for the gutters, as it looks clean and simple. You can pick white for the gutters as an accent color if your home is a dark color. If your home is gray or brown, you may paint the gutters gray or brown as well so they blend in. Use a small amount of top coat on the paintbrush so it spreads thinly on the gutters. Correct any runs in the paint using the brush. You can also apply a thin layer of top coat with a paint sprayer if you’d prefer. Only spray over the gutters once with the top coat so it does not become too thick. Allow 2-4 hours for the top coat to dry completely. If you are using a quick-drying top coat, it may take less time for it to dry. Apply another layer of top coat with a paint brush or a paint sprayer so the color appears even. Once the paint has dried completely, replace the gutters. Make sure you put them back up in order and that they are secure. Stand back and look at the freshly painted gutters. Use a small paint brush dipped in top coat to touch up any spots you may have missed.

summary: Choose an oil-based satin top coat. Select a color that complements your home color. Apply a thin layer of top coat with a paintbrush or a sprayer. Let the paint dry, then apply a second coat. Replace the gutters if you took them down. Touch up the gutters as needed.


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For the first phase, Induction, you avoid eating nearly all carbohydrates. This includes breads, baked goods, grains, potatoes, sugary foods and drinks, fruits, alcohol, etc. This may be hard at first, so prepare yourself by slowly weening off carbs in the days leading up to your Atkin's Diet start date.  You may consume no more that 20 grams of net carbs per day, and most of these carbs should come from vegetables such as asparagus, broccoli, and green beans. About two cups of loosely-packed salad, plus a cup of another vegetable, will equal approximately 20 grams of net carbs from vegetables. In the Induction phase, you should also eat protein at each meal. You can choose from fish, poultry, red meat, pork products, eggs, cheese, etc.  The portion size of these proteins can be generous. You do not need to restrict oils and fats. ” These are low-carb vegetables that are especially beneficial for the first stage of the Atkins Diet, and you are encouraged to eat them throughout the other phases. They include:  Leafy greens such as lettuce and spinach Crisp greens such as cucumbers, celery, broccoli, zucchini and green beans Other vegetables such as peas, eggplant, tomatoes, onions, cauliflower, and peppers. During the Induction phase of the Atkins Diet, you should drink eight glasses of water per day. This is important to avoid dehydration and constipation. If you are beginning the Atkins Diet at the Induction phase, you will need to follow these guidelines for at least two weeks to maximize your transition and weight loss. If you want to or need to lose more weight, you may stay in this phase longer. Knowing ahead of time what you can and will eat while on the Induction phase will help you succeed at the start of the Atkins Diet. It will keep you organized, focused, and on track. A typical menu for this phase might include:  For breakfast: a good source of protein like scrambled eggs, with ingredients like onions and cheese, and 3 breakfast sausages. Coffee, tea, water, or diet soda are acceptable beverages in the Induction phase and throughout the other phases of the Atkins Diet.  For lunch: a salad with a protein such as chicken, and an acceptable beverage. Another option is a bacon cheeseburger (without bun).  For dinner: Salmon, asparagus, and a salad, and an acceptable beverage. Another option is a shrimp cocktail, baked chicken, and a small salad.  Snacks (up to two per day): An Atkins Diet product (these include shakes, granola bars, etc), diet gelatin with artificially-sweetened whipped cream, or a protein-rich, low-carb snack like celery and cheddar cheese.
summary: Eliminate almost all carbohydrates from your diet. Eat generous amounts of protein-rich foods. Focus on “foundation vegetables. Drink plenty of water. Follow the guidelines of the Induction phase for at least two weeks. Develop a menu plan.