Title of the invention: Anode active material for lithium secondary battery and lithium secondary battery containing the same Technical field [One] This application is an application for claiming priority for Korean Patent Application No. 10-2018-0067287 filed on June 12, 2018, and all contents disclosed in the specification and drawings of the application are incorporated herein by reference. [2] The present invention relates to an anode active material for a lithium secondary battery, and more particularly, to an anode active material for a lithium secondary battery with improved lifespan and output performance. [3] Background [4] As technology development and demand for mobile devices increase, the demand for secondary batteries as an energy source is rapidly increasing. Among these secondary batteries, lithium secondary batteries having a high energy density and voltage, a long cycle life, and a low discharge rate are commercialized and widely used. [5] The lithium secondary battery has a structure in which an electrolyte including a lithium salt is impregnated with an electrode assembly in which a porous separator is interposed between a positive electrode and a negative electrode, each of which an active material is applied on an electrode current collector, and the electrode is an active material and a binder. And a slurry in which a conductive material is dispersed in a solvent is applied to a current collector, and dried and rolled. [6] In addition, the basic performance characteristics of a lithium secondary battery, such as capacity, output, and life, are greatly influenced by the anode material. In order to maximize the performance of the battery, the negative electrode active material needs to have an electrochemical reaction potential close to the lithium metal, the reaction reversibility with lithium ions must be high, and the diffusion rate of lithium ions in the active material must be fast. Carbon-based materials are widely used as materials meeting these requirements. [7] The carbon-based active material is excellent in stability and reversibility, but has a limitation in terms of capacity. Therefore, in recent years, a Si-based material having a high theoretical capacity is applied as a negative electrode active material in fields requiring high-capacity batteries such as electric vehicles and hybrid electric vehicles. [8] However, when the Si-based negative active material absorbs and stores lithium, the crystal structure changes and its volume expands. Such volume expansion causes cracking, causing disruption of active material particles or poor contact between the active material and the current collector, and thus a problem of shortening the charge/discharge cycle life of the battery. [9] On the other hand, it is reported that silicon oxide among Si-based negative active materials exhibits less expansion and stable life in battery reactions than silicon. However, due to the low conductivity and specific surface area peculiar to silicon oxide, and expansion/contraction accompanying charging and discharging, it still does not show a stable life in battery performance. [10] Detailed description of the invention Technical challenge [11] Accordingly, the present invention is to solve the above problems, and one object of the present invention is to provide an anode active material made of a silicon oxide material with improved output performance as well as lifetime performance. [12] Another object of the present invention is to provide a negative electrode including the negative electrode active material and a lithium secondary battery having the same. [13] Means of solving the task [14] According to an aspect of the present invention, a silicon oxide is included, and the silicon oxide has a full width at half maximum (FWHM) of 2 to 6 in a particle size distribution having an average particle diameter (D50) of 1 to 20 µm. An anode active material for a phosphorus lithium secondary battery is provided. [15] The half width of the silicon oxide may be in the range of 3 to 5. [16] The silicon oxide may be represented by SiO x (0