(a)The time-independent, normalized wave function for the one-dimensional quantum harmonic oscillator in its ground state is given by:ψ0(x) = (a/pi)1/4 e−ax2/2where a = (x)0=momega/h, m is the mass of the oscillator, ω is the angular frequency of the oscillator, and ℏ is the reduced Planck constant, :h/2pi Let the symbol (q)s denote the expectation value of the quantity q for the state ψs(x). What is the expectation value (x)0? (Use the following as necessary: a.)(b) The time-independent, normalized wave function for the one-dimensional quantum harmonic oscillator's first excited state is given byψ1(x) = (4a^3/pi) 1/4xe−ax2/2What is the expectation value (x)1 ? (Use the following as necessary: a.)(x)1 =(c) In quantum mechanics, a particle does not have to be in a "definite" state. It can be in a "mixed" state, or superposition of states. Consider a quantum harmonic oscillator with the wave function:ψ01(x) = 1/sqrt2[ψ0(x) + ψ1(x)](x)01 = where ψ0(x) and ψ1(x) are given above. This represents a particle with a non-zero (and in this case, equal) probability of being found either in the ground state or first excited state, before a measurement is taken. What is the expectation value (x)01 for this wave function? (Use the following as necessary: a.)ψ01(x) =

Awater balloon launcher uses an elastic band with a spring constant of 115 n/m to use thee launcher you stretch thee band back with a balloon n it the water balloons have a mass of 1.3 kg a) if you stretch the band by 0.8 m, what elastic force will the band exert? b) with the band stretched 0.8 m, how much elastic potential energy is stored in the spring? c) if you release the band, it pushes forward. what is the kinetic energy of the balloon when it reaches the natural length of the band? d) what is the speed of the balloon when it reaches the natural length of the band?

Need asap which of these is an example of a hypothesis? (2 points) a. adults were not interviewed b. the investigation was time consuming c. the source of information was biased d. very few teenagers were interviewed scientists in different parts of the world have conducted experiments to find the speed of light in vacuum. if the results of the experiments are identical, they would most likely be (2 points) a.valid b. biased c. unreliable d. non-observable which of these questions can be answered using science? (2 points) a. what is the best career? b. does water exist on venus? c. should the use of automobiles be stopped? d. which is the most interesting subject to study? the models can be best used to (2 points) recreate something which is easily observed in nature prove that all atomic theories have the same meaning demonstrate the transformation of atomic theory into law represent the locations of subatomic particles in different atomic theories 22. (bws.06) scientists earlier believed that the lowest measurable temperature is the freezing point of ice. however, modern scientists believe that temperatures below the freezing point of ice can also exist. what best accounts for these different opinions? (2 points) scientists propose contradictory ideas to include all possibilities scientists come up with different hypotheses without enough evidence scientists propose different ideas to avoid repetition of scientific knowledge scientists having different interests may interpret the same data in different ways based on the graph, what is the most likely mass of an apple chosen randomly from the basket? (2 points) between 0.10 kg and 0.12 kg between 0.12 kg and 0.14 kg between 0.14 kg and 0.16 kg between 0.16 kg and 0.18 kg a scientist studies a model of a widely accepted theory about the position of planets and sun. the model would most likely the scientist to (2 points) prove that the theory would not change in the future demonstrate how the theory can be changed into a law understand facts which cannot be easily observed prove that all other facts about the universe are incorrect one scientist discovered a new theory on the evolution of the universe. what is the next step for the scientist to take? (2 points) transform the results of the theory into universal laws of nature inform the scientific community so they can verify the results call a press conference to make the discovery popular among people encourage scientists worldwide to find an appropriate application for the results the students' observations are listed below. when an iron nail is taken near the north pole (n) of the bar magnet, it is pulled towards the magnet. when an iron nail is taken near the south pole (s) of the bar magnet, it is pulled towards the magnet. the experiment was repeated by several students using different bar magnets. based on the investigations, which of these theories would the students most likely propose? (2 points) magnets attract iron nails the poles of a magnet attract all materials iron nails are attracted towards all materials iron nails have the same properties as magnets

The chart shows the costs and shipping times for materials that a company needs to build a new product. which describes the best trade-off if the company needs to start building their product within the next two years? they should order the domestic materials because it is always best to choose the fastest shipping time. they should order the imported materials because it is always best to choose the lowest cost for materials. since the shipping time is longer, they should order the domestic materials because the additional cost is worth it to get the materials in time. even though the shipping time is longer, they should order the imported materials because they are less expensive and should arrive in plenty of time to build the product.