In one dimension, compare the plane wave solutions to the heat equation ?T/?t = a? 2 T/?x
Question:
In one dimension, compare the plane wave solutions to the heat equation ?T/?t = a?2T/?x2 with plane wave solutions to the free Schr?dinger equation
Show that the heat equation has real solutions that oscillate in space and decay in time, whereas the Schr?dinger equation has complex solutions that oscillate in both space and time.
Transcribed Image Text:
iðy /ôt = -(ħ/2m)ớyldx²
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 70% (10 reviews)
Look for plain wave solution of the form Tx t e ikx f t S...View the full answer
Answered By
Nyron Beeput
I am an active educator and professional tutor with substantial experience in Biology and General Science. The past two years I have been tutoring online intensively with high school and college students. I have been teaching for four years and this experience has helped me to hone skills such as patience, dedication and flexibility. I work at the pace of my students and ensure that they understand.
My method of using real life examples that my students can relate to has helped them grasp concepts more readily. I also help students learn how to apply their knowledge and they appreciate that very much.
4.00+
1+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Physics questions
-
A particle moving in one dimension (the x-axis) is described by the wave function where b = 2.00 m-1,A > 0, and the +x-axis points toward the right(a) Determine A so that the wave function is...
-
Consider a free-particle wave packet in one dimension. At 1= 0 it satisfies the minimum uncertainty relation in addition, we know Using the Heisenberg picture, obtain , as a function of t(t ? 0) when...
-
Consider a particle moving in one dimension under the influence of a potential V(x). Suppose its wave function can be written as exp [iS (x, t) / h]. Prove that S(x, t) satisfies the classical...
-
What are the upper and lower 2.5th percentiles for a chi-square distribution with 2 df? What notation is used to denote these percentiles? Pulmonary Disease The data in Table 6.10 concern the mean...
-
A motorcycle is traveling up one side of a hill and down the other side. The crest of the hill is a circular arc with a radius of 45.0 m. Determine the maximum speed that the cycle can have while...
-
Compare/contrast Julius Caesar with Yitzhak Rabin leader and summarize the findings in the following manner: Introduction Background on Julius Caesar Background on Yitzhak Rabin Comparison of both...
-
You are considering the controls over a client's personnel and payroll activities. System documentation was accomplished with a questionnaire and a narrative memorandum and, in conjunction with a...
-
Octavia Corp.'s products are manufactured in three separate departments: Molding, Curing, and Finishing. Materials are introduced in Molding; additional material is added in Curing. The following...
-
Explain by giving examples the causes of the differences between taxable income and accounting income ( 5 Marks ) b . Dolphin Company Limited has results of its operations for the year 2 0 1 4 as...
-
1. What type of team(s) do these employee teams appear to be? Explain. 2. As this story illustrated, sometimes it may take a long time for a team to reach its goal. As a manager, how would you...
-
1 Plancks constant is very small on the scale of human affairs. Compare the angular momentum of a childs marble spinning at 60 rpm with Plancks constant. Compare the energy of the same marble...
-
Nuclear forces are so strong that they keep protons and neutrons in a spherical region a few femtometers in radius (1 fm = 10 15 m). To get a crude idea of the energy scales involved in nuclear...
-
There is no doubt that Microsoft Office (including Access & Excel) is the industry leader for office productivity software - it can be found in almost all businesses. But, recently there has been a...
-
Maury completed a bicycle race 1.5 hours faster than Vince at an average speed of 16 miles per hour. Vince completed the same race at an average speed of 12 miles per hour. How many miles was the...
-
If $125 is invested at an interest rate of 18% per year and is compounded continuously, how much will the investment be worth in 2 years? Use the continuous compound interest formula
-
You are buying carpet to cover a room that measures 45ft by 42ft. The carpet cost $22 per square yard. How much will the carpe cost?
-
Ash has $8,000 in a savings account. The interest rate is 3% compounded once a year. To the nearest cent, how much will he have in his account in 4 years?
-
A six-sided die with sides labeled 1 through 6 will be rolled once. Each number is equally likely to be rolled. What is the probability of rolling a number greater than 2 ? Write your answer as a...
-
Consider a random binary pulse waveform as an alyzed in Example 7.6, but with half-cosine pulses given by p(t) = cos(2t / 2T)II(t / T). Obtain and sketch the auto correlation function for the two...
-
How can you tell from the vertex form y = a(x - h) 2 + k whether a quadratic function has no real zeros?
-
For its size, the common flea is one of the most accomplished jumpers in the animal world. A 2.0-mm-long, 0.50-mg critter can reach a height of 20 cm in a single leap. (a) Neglecting air drag, what...
-
The maximum energy that a bone can absorb without breaking depends on its characteristics, such as its cross-sectional area and its elasticity. For healthy human leg bones of approximately 6.0 cm2...
-
Tendons are strong elastic fibers that attach muscles to bones. To a reasonable approximation, they obey Hookes law. In laboratory tests on a particular tendon, it was found that, when a 250-g object...
-
New Flyer Industries has decided to expand its production of hybrid transit buses. The firm expects incremental cash flows of? $40 million per year for the next 10 years. The upfront cost of the...
-
Calculate the mean, mode, median, standard deviation, and range for the Graduation Rate, Salary After Completing Program, and Annual Cost. our response to each of these should include only the mean,...
-
1. Propel Corporation plans to make an investment, initially funded completely with debt. The investment requires an initial upfront cost of $49.8 million. The free cash flows of the investment and...
Study smarter with the SolutionInn App