Which of the following statement is True?
A: [img=20x18]1803bd52d74f76c.png[/img] is an eigenvalue of the position operator [img=11x19]1803bd52df60698.png[/img] .
B: [img=70x25]1803bd52e788f4d.png[/img] is an eigenfunction of the position operator [img=16x19]1803bd52ef5ee5a.png[/img]
C: The position operator [img=11x19]1803bd52f76293f.png[/img] is a linear operator.
D: The operator [img=28x18]1803bd5300119fc.png[/img] is a linear operator.
A: [img=20x18]1803bd52d74f76c.png[/img] is an eigenvalue of the position operator [img=11x19]1803bd52df60698.png[/img] .
B: [img=70x25]1803bd52e788f4d.png[/img] is an eigenfunction of the position operator [img=16x19]1803bd52ef5ee5a.png[/img]
C: The position operator [img=11x19]1803bd52f76293f.png[/img] is a linear operator.
D: The operator [img=28x18]1803bd5300119fc.png[/img] is a linear operator.
举一反三
- Define an inner product by [img=183x51]18034570c994c23.png[/img] and the Hilbert space [img=314x25]18034570d4e10d1.png[/img]. The operator [img=110x49]18034570de689c2.png[/img] is a self-adjoint operator.
- 令F(x):x是有理数,G(x):x是实数。将命题“所有的有理数都是实数,但有的有实数不是有理数”符号化为() 未知类型：{'options': ['17e0a83a4157352.jpgx(F(x)∧G(x))∧[img=8x14]17e0a83a35505d4.jpg[/img]x(G(x)[img=14x9]17e0a73094b5dcf.jpg[/img][img=10x11]17e0a839b915354.jpg[/img]F(x))', ' [img=8x14]17e0a83a4157352.jpg[/img]x(F(x)[img=14x9]17e0a73094b5dcf.jpg[/img]G(x))∧[img=8x14]17e0a83a35505d4.jpg[/img]x(G(x)∧[img=10x11]17e0a839b915354.jpg[/img]F(x))', ' [img=8x14]17e0a83a4157352.jpg[/img]x(F(x)∧G(x))∧[img=8x14]17e0a83a35505d4.jpg[/img]x(G(x)∧[img=10x11]17e0a839b915354.jpg[/img]F(x))', ' [img=8x14]17e0a83a4157352.jpg[/img]x(F(x)[img=14x9]17e0a73094b5dcf.jpg[/img]G(x))∧[img=8x14]17e0a83a35505d4.jpg[/img]x(G(x)[img=14x9]17e0a73094b5dcf.jpg[/img][img=10x11]17e0a839b915354.jpg[/img]F(x))'], 'type': 102}
- 在下列命题中:如果f(x)=[img=28x44]17e0bf9914bb2f1.png[/img],那么[img=27x29]17e0bf97582597b.png[/img]f(x)=0;如果f(x)=[img=28x44]17e0bf992111a1c.png[/img],那么[img=27x29]17e0bf97582597b.png[/img]f(x)=0;如果f(x)=[img=55x44]17e0bf992d8de0a.png[/img],那么[img=29x29]17e0bf9939482bb.png[/img]f(x)不存在;如果f(x)=[img=87x53]17e0bf99450fa82.png[/img],那么[img=27x29]17e0bf97582597b.png[/img]f(x)=0。其中错误命题的个数是( A: 0 B: 1 C: 2 D: 3
- 若f(x)+f(-x)=0, 则[img=95x39]17da608af452d96.jpg[/img]. 若f(x)=f(-x), 则 [img=170x38]17da60541207426.jpg[/img]
- 下列函数中为同一个函数的是() 未知类型：{'options': ['f(x)=x,g(x)=[img=25x39]17e43f7e294a229.png[/img]', ' f(x)=x,g(x)=[img=39x24]17e43f7e31cdea3.jpg[/img]', ' f(x)=x,g(x)=[img=35x25]17e43f7e3c419e9.png[/img]', ' f(x)=|x|,g(x)=[img=35x25]17e43f7e3c419e9.png[/img]'], 'type': 102}