Concept explainers
Why a particle confined to a finite region cannot have zero energy.
Explanation of Solution
If the ground state-state energy of a particle that confined to a finite region is zero, then it will violate the uncertainty principle. Because of the zero kinetic energy, the particle has zero momentum and then its position is absolutely determined.
That means the uncertainty in position is equal to the width of the potential well (region), then the uncertainty relation becomes
Therefore, the particle confined to a finite region cannot have zero energy.
Want to see more full solutions like this?
Chapter 35 Solutions
Modified Mastering Physics With Pearson Etext -- Standalone Access Card -- For Essential University Physics (3rd Edition)
- Can a quantum particle 'escape' from an infinite potential well like that in a box? Why? Why not?arrow_forwardCan the magnitude of a wave function (*(x,t)(x,t)) be a negative number? Explain.arrow_forwardWhich one of the following functions, and why, qualifies to be a wave function of a particle that can move along the entire real axis? (x)=Aex2; (x)=Aex; (x)=Atanx; (x)=A(sinx)/x; (x)=Ae|x|arrow_forward
- Consider an infinite square well with wall boundaries x=0 and x=L. Show that the function (x)=Asinkx is the solution to the stationary Schrödinger equation for the particle in a box only if k=2mE/h. Explain why this is an acceptable wave function only if k is an integer multiple of /L.arrow_forwardFind the expectation value of the square of the momentum squared for the particle in the state, (x,t)=Aei(kxt). What conclusion can you draw from your solution?arrow_forwardSuppose a wave function is discontinuous at some point. Can this function represent a quantum state of some physical particle? Why? Why not?arrow_forward
- Suppose an infinite square well extends from L/2 to +L/2 . Solve the time-independent Schrödinger's equation to find the allowed energies and stationary states of a particle with mass m that is confined to this well. Then show that these solutions can be obtained by making the coordinate transformation x=xL/2 for the solutions obtained for the well extending between 0 and L.arrow_forwardA particle of mass m confined to a box of width L is in its first excited state 2(x). (a) Find its average position (which is the expectation value of the position). (b) Where is the particle most likely to found?arrow_forwardFind the expectation value of the kinetic energy for the particle in the state, (x,t)=Aei(kxt). What conclusion can you draw from your solution?arrow_forward
- A particle of mass m is confined to a box of width L. If the particle is in the first excited state, what are the probabilities of finding the particle in a region of width0.020 L around the given point x: (a) x=0.25L; (b) x=040L; (c) 0.75L and (d) x=0.90L.arrow_forwardCan the particle in a one-dimensional box have energy degeneracy? Explain your answer in wordsarrow_forwardIs the ground-state energy of a proton trapped in a onedimensional infinite potential well greater than, less than, or equal to that of an electron trapped in the same potential well?arrow_forward
- University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStaxModern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning