The k = 0 state of the quantum mechanical free particle can be considered a state with a zero point energy equal to zero. the zero point energy of the particle in a box is not zero. what changes can you make to the particle in a box so that it approaches the free particle behavior? you are not allowed the trivial choice to remove the walls of the box. justify your answer with appropriate equations or formulae. this discuss in terms of the quantum classical correspondence principle.

Much of the information taught in earth-space science would not be available if it weren’t for our remote sensing abilities. explain two ways our remote sensing strategies contribute to our knowledge of these topics.

Aheat engine running backward is called a refrigerator if its purpose is to extract heat from a cold reservoir. the same engine running backward is called a heat pump if its purpose is to exhaust warm air into the hot reservoir. heat pumps are widely used for home heating. you can think of a heat pump as a refrigerator that is cooling the already cold outdoors and, with its exhaust heat qh, warming the indoors. perhaps this seems a little silly, but consider the following. electricity can be directly used to heat a home by passing an electric current through a heating coil. this is a direct, 100% conversion of work to heat. that is, 19.0 \rm kw of electric power (generated by doing work at the rate 19.0 kj/s at the power plant) produces heat energy inside the home at a rate of 19.0 kj/s. suppose that the neighbor's home has a heat pump with a coefficient of performance of 4.00, a realistic value. note: with a refrigerator, "what you get" is heat removed. but with a heat pump, "what you get" is heat delivered. so the coefficient of performance of a heat pump is k=qh/win. an average price for electricity is about 40 mj per dollar. a furnace or heat pump will run typically 200 hours per month during the winter. what does one month's heating cost in the home with a 16.0 kw electric heater? what does one month's heating cost in the home of a neighbor who uses a heat pump to provide the same amount of heating?

The frequencies refer to the sample data collected from a population of interest when performing a hypothesis test comparing two or more population proportions.